{"id":19,"date":"2012-09-05T11:22:25","date_gmt":"2012-09-05T15:22:25","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/template\/?page_id=19"},"modified":"2026-09-23T21:46:17","modified_gmt":"2026-09-24T01:46:17","slug":"publications","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/leizhang\/publications\/","title":{"rendered":"Publications"},"content":{"rendered":"\n<section class=\"fullwidth-text-block\"><div class=\"container px-0\"><div class=\"row align-items-start\"><div class=\"col-12\">\n<h1 class=\"wp-block-heading\">Publications<\/h1>\n\n\n\n<h4 class=\"wp-block-heading\"><em>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Nonlinear Partial Differential Equations, Geometric Analysis and Medical Imaging Problems. <\/em><\/h4>\n\n\n\n<h4 class=\"wp-block-heading\"><em>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; This links to my mathscinet page:<\/em><\/h4>\n\n\n\n<h4 class=\"wp-block-heading\"><em>&nbsp; &nbsp;&nbsp; &nbsp;&nbsp; &nbsp;&nbsp; &nbsp;&nbsp; <a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/author?authorId=700853\">https:\/\/mathscinet.ams.org\/mathscinet\/author?authorId=700853<\/a><\/em><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><i>1.Classification of conformal metrics on $R^2_+$ with constant Gauss curvature and geodesic curvature on the boundary under various integral finiteness assumptions,<strong> Calc. Var. Partial Differential Equations,<\/strong> 16, (2003), no.4, 405-430.<\/i><\/li>\n\n\n\n<li><i> <i>2. Refined Asymptotic Estimates for Conformal Scalar Curvature Equation Via Moving Sphere Method, <strong>J. Functional Analysis,<\/strong> 192, (2002), no.2, 491-516. <\/i><\/i><\/li>\n\n\n\n<li><i><i> <i>3. Arbitrarily Large Solutions of the Scalar Curvature Equation at an Isolated Singularity (with S.Taliaferro), <strong>Proc. Amer. Math. Soc<\/strong>, 131 (2003), no.9, 2985-2902. <\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>4. Liouville type theorems and Harnack type inequalities for semi-linear elliptic equations (with Y.Y. Li), <strong>J. Anal. Math<\/strong>, 90(2003), 27-87. <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>5. A Harnack type inequality for the Yamabe equation in low dimensions (with Y. Y. Li),<strong> Calc. Var. Partial Differential Equations<\/strong> 20 (2004), 133-151. <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>6. Compactness of solutions to the Yamabe problem (with Y. Y. Li), <strong>C. R. Acad. Sci. Paris<\/strong>, Ser. I 338 (2004), 693-695. <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>7. Compactness of solutions to the Yamabe problem II (with Y. Y. Li), <strong>Calc. Var. Partial Differential Equations<\/strong>, 24 (2005), no. 2, 185&#8211;237. <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>8. A priori estimates and uniqueness results for some mean-field equation, (with M. Lucia), <strong>J. Differential Equations<\/strong>, 217 (2005), no. 1, 154&#8211;178. <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>9. Asymptotic symmetry for conformal scalar curvature equation with singularities (with S.Taliaferro). <strong>Calc. Var. Partial Differential Equations<\/strong>, 26, (2006) no 4: 401-428. <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>10. Blowup solutions for some nonlinear elliptic equations involving exponential nonlinearities, <strong>Comm. Math. Phys<\/strong>, 268, (2006) no 1: 105-133. <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>11. Compactness of solutions to the Yamabe problem III (with Y. Y. Li). <strong>J. Functional Analysis<\/strong>, 245 (2007) 438-474. <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>12. Harnack Type Inequalities for conformal scalar curvature equation, <strong>Math. Ann,<\/strong> (2007) 339, 195-220. <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>13. Prescribing curvatures on three dimensional Riemannian manifolds with boundaries, <strong>Trans. Amer. Math. Soc.<\/strong> 361 (2009), 3463-3481. <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>14. Asymptotic behavior of blowup solutions for elliptic equations with exponential nonlinearity and singular data, <strong>Communications in Contemporary&nbsp; mathematics<\/strong>, vol 11, issue 3, June 2009, 395-411. Also available at <a href=\"https:\/\/people.clas.ufl.edu\/leizhang\/content-removed\/\">arXiv:0810.5143<\/a>. <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>15. A priori estimate for a family of semi-linear elliptic equations with critical nonlinearity, <strong>Journal of Differential Equations<\/strong>, 247 (2009) 1334-1353, also available at <a href=\"https:\/\/arxiv.org\/abs\/0810.5140\">arXiv:0810.5140&nbsp; <\/a><\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>16. The profile of bubbling solutions of a class of fourth order geometric equations on 4-manifolds, (with G. Weinstein), <strong>Journal of Functional Analysis<\/strong>, Volume 257 (2009), Issue 12, 3895-3929, available at <a href=\"https:\/\/arxiv.org\/abs\/0810.4879\">arXiv: 0810.4879&nbsp; <\/a><\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>17. Profile of bubbling solutions to a Liouville system (with Chang-shou Lin),<strong> Annales de l&#8217;Institut Henri Poincare \/ Analyse non lineaire,<\/strong> Volume 27, Issue 1, January-February 2010, Pages 117-143, available at <a href=\"https:\/\/arxiv.org\/abs\/0903.0381\">arxiv 0903.0381<\/a>:&nbsp; <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>18. The monotonicity theorems for the Laplace-Beltrami operator, (with E. Teixeira), <strong>Advances in Mathematics<\/strong>, Vol. 226, Issue 2, 30 January 2011, pp. 1259-1284.&nbsp; <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>19. A local parabolic monotonicity formula on Riemannian manifolds (with E. Teixeira), <strong>Journal of Geometric Analysis<\/strong>: Volume 21, Issue 3 (2011), Page 513-526, available at arxiv 0906.1483:&nbsp; <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i> 20. A topological degree counting for some Liouville systems of mean field equations (with Chang-shou Lin), <strong>Comm. Pure Appl. Math.<\/strong> volume 64, Issue 4, pages 556\u2013590, April 2011.&nbsp; <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>21. An elliptic variational problem involving level surface area on Riemannian manifolds (with E. Teixeira),<strong> Revista Matematica Iberoamericana<\/strong> 28 (2012), no. 3, 759\u2013772. <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>22. Local gradient estimate for p-harmonic functions on Riemannian manifolds (with X. Wang ), <strong>Comm. Anal. Geom,<\/strong> volume 19 (2011), no 4, 759-772, also available at arxiv 1010.2889.&nbsp; <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>23. Monge-Ampere equations on exterior domains (with Jiguang Bao, Haigang Li ), <strong>Cal. Var. PDE<\/strong>.52 (2015), no. 1-2, 39\u201363. , arxiv: 1304:2415<a href=\"http:\/\/arxiv.org\/abs\/1304.2415\">&nbsp;http:\/\/arxiv.org\/abs\/1304.2415 <\/a><\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>24. On Liouville systems at critical parameters, Part 1: One bubble. (with Chang-shou Lin), <strong>Journal of Functional Analysis<\/strong> vol. 264 (2013) 2584-2636, arxiv: 1302.1147. <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>25. Classification of blowup limits for SU(3) singular Toda systems (with Chang-shou Lin and Juncheng Wei), <strong>Analysis and PDE<\/strong>, Vol. 8 (2015), No. 4, 807\u2013837. , arxiv:1303:4167&nbsp;<a href=\"http:\/\/arxiv.org\/abs\/1303.4167\"> http:\/\/arxiv.org\/abs\/1303.4167 <\/a><\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>26. Classification of Radial Solutions to Liouville Systems with Singularities (with Chang-shou Lin), <strong>Discrete and Continuous Dynamical System<\/strong>, Volume 34, Issue 6, June 2014, <\/i><\/i><\/i><\/i><i><i><i><i>Pages: 2617 &#8211; 2637 arxiv: 1302:3866.<a href=\"https:\/\/people.clas.ufl.edu\/leizhang\/content-removed\/\">lin-zhang-dcds-a<\/a> <\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>27. Local profile of fully bubbling solutions to SU(n+1) Toda systems (with Chang-shou Lin and Juncheng Wei), <strong>Journal of European Mathematical Society,<\/strong> vol 18, issue 8, 1707-1728, 2016.&nbsp; arxiv: 1308.1579<a href=\"http:\/\/arxiv.org\/abs\/1308.1579\">&nbsp;http:\/\/arxiv.org\/abs\/1308.1579 <\/a><\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>28. A Harnack-Type Inequality for a Prescribing Curvature equation on a Domain with Boundary (with Mathew Gluck and Ying Guo),&nbsp; <a href=\"http:\/\/www.ams.org\/mathscinet\/search\/journaldoc.html?cn=Adv_Nonlinear_Stud\"> <em><strong>Adv. Nonlinear Stud<\/strong>.<\/em><\/a> <a href=\"http:\/\/www.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=323975\"> 14 <\/a><a href=\"http:\/\/www.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=323975\"> (2014), <\/a><a href=\"http:\/\/www.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=323975\"> no. 3,<\/a> 709\u2013746. arxiv: 1309.1135. <a href=\"https:\/\/people.clas.ufl.edu\/leizhang\/content-removed\/\">bry-harnack-gluck-guo<\/a><\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li><i><i><i> <i>29. Energy estimates for a class of semilinear elliptic equations on half Euclidean balls (with Ying Guo),&nbsp; <\/i><\/i><\/i><\/i><i><i><i><i><i><i><i><i><i><strong>Revista Matematica Iberoamericana,<\/strong> vol 31, issue 4, 2015, 1141-1166.&nbsp; <\/i><\/i><\/i><\/i><\/i><\/i><\/i><\/i><\/i><i><i><i><i>arxiv: 1309.5081 . <a href=\"https:\/\/people.clas.ufl.edu\/leizhang\/content-removed\/\">guo-zhang<\/a><\/i><\/i><\/i><\/i><\/li>\n\n\n\n<li>30. <span class=\"title\">Blowup solutions of elliptic systems in two dimensional spaces.<\/span> <em> Proceedings of the Sixth International Congress of Chinese Mathematicians. Vol. II, <\/em> 617\u2013624, <a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/series.html?id=5161\"><strong>Adv. Lect. Math.<\/strong> (ALM), 37,<\/a> <em>Int. Press, Somerville, MA,<\/em> 2017. arxiv: 1311.0694.<\/li>\n\n\n\n<li>31. Convergence rate, location and $partial_z^2$ condition for fully bubbling solutions to $SU(n+1)$Toda systems (with Chang-shou Lin and Juncheng Wei),&nbsp;<strong> Advances in Mathematics.<\/strong> v 285, 5,&nbsp; November 2015, Pages 1189\u20131224&nbsp; arxiv: 1410.7410&nbsp;<a title=\"PDF\" href=\"http:\/\/arxiv.org\/abs\/1410.7410\"> http:\/\/arxiv.org\/abs\/1410.7410<\/a><\/li>\n\n\n\n<li>32. Classification of solutions to a critically nonlinear system of elliptic equations on Euclidean half-space, (with Mathew Gluck), <span style=\"font-family: Arial,Helvetica,sans-serif\"><em><strong>J. Part. Diff. Eq.,<\/strong> 28 (2015), pp. 74-94.<\/em><\/span><br><div dir=\"ltr\"><a href=\"https:\/\/people.clas.ufl.edu\/leizhang\/content-removed\/\">http:\/\/arxiv.org\/pdf\/1401.2666.pdf<\/a><\/div><\/li>\n\n\n\n<li>33. Global Monge-Ampere equations with asymptotically periodic data (with Eduardo Teixeira), <strong>Indiana Univ. Math. J<\/strong>. <strong>65<\/strong> No. 2 (2016), 399\u2013422. arxiv: 1406.1386. <a href=\"http:\/\/arxiv.org\/abs\/1406.1386\">http:\/\/arxiv.org\/abs\/1406.1386<\/a><\/li>\n\n\n\n<li>34. Vanishing estimates for fully bubbling solutions of SU(n+1) Toda systems at a singular source. <strong>Int. Math. Res. Not. IMRN <\/strong>2020, no. 18, 5774\u20135795.<\/li>\n\n\n\n<li>35. Energy concentration for Singular $B_2$ and $G_2$ Toda systems (with Chang-shou Lin), <cite><strong> <abbr class=\"slug-jnl-abbrev\" title=\"International Mathematics Research Notices\"> Int Math Res Notices<\/abbr><\/strong> <span class=\"slug-doi-wrapper\"><span class=\"slug-doi\" title=\"10.1093\/imrn\/rnv304\">. 2016, No. 16, pp. 5076\u20135105<\/span> <\/span> <\/cite>..<a href=\"http:\/\/arxiv.org\/abs\/1505.03012\">http:\/\/arxiv.org\/abs\/1505.03012<\/a><\/li>\n\n\n\n<li>36. Global solutions and exterior Dirichlet problem for Monge-Ampere equations in $mathbb R^2$ (with J. G. Bao and H. G. Li ) ,&nbsp; <strong>Differential Integral Equations<\/strong> 29 (2016), no. 5-6, 563\u2013582.<\/li>\n\n\n\n<li>37. Optimal $C^{1,alpha}$ estimates for a class of elliptic quasilinear equations (with Damiao Araujo), <a href=\"http:\/\/arxiv.org\/abs\/1507.06898\">http:\/\/arxiv.org\/abs\/1507.06898<\/a>&nbsp; <i><a href=\"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219199719500147\"><strong>Commun. Contemp. Math<\/strong>. 22 (2020), no. 5, 1950014,<\/a> 19 pp<\/i><\/li>\n\n\n\n<li>38. The domain geometry and the bubbling phenomenon of rank two Gauge theory (with Hsin-Yuan Huang). <a href=\"http:\/\/arxiv.org\/abs\/1510.07055\">http:\/\/arxiv.org\/abs\/1510.07055<\/a>&nbsp; <a href=\"http:\/\/www.ams.org\/mathscinet\/search\/journaldoc.html?id=1529\"> <em><strong>Comm. Math. Phys<\/strong>.<\/em><\/a> <a href=\"http:\/\/www.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=348677&amp;sort=oldest\"> 349 <\/a><a href=\"http:\/\/www.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=348677&amp;sort=oldest\"> (2017), <\/a><a href=\"http:\/\/www.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=348677&amp;sort=oldest\"> no. 1,<\/a> 393\u2013424.<\/li>\n\n\n\n<li>39. On Rank Two Toda System with Arbitrary Singularities: Local Mass and A priori Bounds (with C. S. Lin and J. C. Wei, Wen Yang). <a href=\"http:\/\/dx.doi.org\/\"><strong>Analysis &amp; PDE<\/strong> vol 11, no 4. (2018) 873\u2013898<\/a>&nbsp; <a href=\"http:\/\/arxiv.org\/abs\/1609.02772\">http:\/\/arxiv.org\/abs\/1609.02772 <\/a><\/li>\n\n\n\n<li>40. Degree counting for Toda system with simple singularity: One point blow up, (with Youngae Lee, Chang-shou Lin, Wen Yang), <strong><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/journaldoc.html?id=204\"> <em>J. Differential Equations<\/em><\/a><\/strong> <a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=425683\"> 268 <\/a><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=425683\"> (2020), <\/a><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=425683\"> no. 5,<\/a> 2163\u20132209. &nbsp; .<a href=\"http:\/\/arxiv.org\/abs\/1707.07156\">http:\/\/arxiv.org\/abs\/1707.07156<\/a><\/li>\n\n\n\n<li>41.Non-degeneracy of Gauss curvature equation with negative conic singularity (with Juncheng Wei). <span style=\"font-size: small\"><strong>Pacific Journal of Mathematics<\/strong> 297-2 (2018), 455&#8211;475. DOI 10.2140\/pjm.2018.297.455<\/span>.&nbsp;&nbsp; <a href=\"https:\/\/arxiv.org\/abs\/1706.10264\">https:\/\/arxiv.org\/abs\/1706.10264<\/a><\/li>\n\n\n\n<li>42. Gu, Yi&nbsp;<span class=\"instInfo\"><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/institution.html?code=1-FL\">(1-FL)<\/a><\/span>; Zhang, Lei&nbsp;<span class=\"instInfo\"><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/institution.html?code=1-FL\">(1-FL)<\/a><\/span>;<br><span class=\"title\">Degree counting theorems for singular Liouville systems.<\/span><br><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/journaldoc.html?id=5905\"><em><strong>Ann. Sc. Norm. Super. Pisa Cl. Sci.<\/strong> (5)<\/em><\/a>&nbsp;<a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=451935\">21&nbsp;<\/a><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=451935\">(2020),&nbsp;<\/a>1103\u20131135.<a href=\"https:\/\/arxiv.org\/abs\/1811.00190\">https:\/\/arxiv.org\/abs\/1811.00190<\/a><\/li>\n\n\n\n<li>43. Estimates for Liouville equation with quantized singularities, with Juncheng Wei, <strong><a href=\"https:\/\/www.journals.elsevier.com\/advances-in-mathematics\">Advances in Mathematics<\/a><\/strong>, <a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=446972\">380&nbsp;<\/a><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=446972\">(2021),&nbsp;<\/a>107606.&nbsp; <a href=\"https:\/\/arxiv.org\/abs\/1905.04123\">https:\/\/arxiv.org\/abs\/1905.04123<\/a><\/li>\n\n\n\n<li>44. Uniqueness of bubbling solutions of mean field equations with non-quantized singularities, with Lina Wu, <a href=\"https:\/\/arxiv.org\/abs\/1906.05914\"><strong>Commun. Contemp. Math<\/strong>. 23 (2021), no. 4, 2050038, 39 pp.<\/a>&nbsp;&nbsp;&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/1906.05914\">https:\/\/arxiv.org\/abs\/1906.05914.&nbsp;<\/a><\/li>\n\n\n\n<li>45. Estimates of bubbling solutions of $SU(3)$ Toda systems at critical parameters-part 1 (with Lina Wu), <strong><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/journaldoc.html?id=5170\"><em>SIAM J. Math. Anal.<\/em><\/a>&nbsp;<\/strong><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=441871\">52&nbsp;<\/a><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=441871\">(2020),&nbsp;<\/a><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=441871\">no. 4,<\/a>&nbsp;3738\u20133776.&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/1912.12071\">https:\/\/arxiv.org\/abs\/1912.12071<\/a><\/li>\n\n\n\n<li>46.&nbsp; Isolated singularities of solutions to the Yamabe equation in dimension 6 (with Jingang Xiong),&nbsp;<strong><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/journaldoc.html?id=6356\"><em>Int. Math. Res. Not. IMRN<\/em><\/a>&nbsp;<\/strong><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=460144\"><span class=\"volyear\">2022,&nbsp;<\/span><\/a><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=460144\">no. 12,<\/a>&nbsp;9571\u20139597.&nbsp;<a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/mscdoc.html?code=35J65\">35J65<\/a> <a href=\"https:\/\/arxiv.org\/abs\/2006.13279\">https:\/\/arxiv.org\/abs\/2006.13279<\/a><\/li>\n\n\n\n<li>47. Asymptotic behavior of solutions to the Yamabe equation with an asymptotically flat metric (with Zhengchao Han and Jingang Xiong), <strong><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/journaldoc.html?id=3612\"><em>J. Funct. Anal.<\/em><\/a><\/strong>&nbsp;<a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=468290\">285&nbsp;<\/a><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=468290\">(2023),&nbsp;<\/a><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=468290\">no. 4,<\/a>&nbsp;Paper No. 109982, 55 pp. &nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2106.13380\">https:\/\/arxiv.org\/abs\/2106.13380<\/a><\/li>\n\n\n\n<li>48. On Liouville systems at critical parameters, Part II: Multiple bubbles (with Hsin-Yuan Huang),&nbsp;<strong><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/journaldoc.html?id=4611\"><em>Calc. Var. Partial Differential Equations<\/em><\/a><\/strong>&nbsp;<a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=454856\">61&nbsp;<\/a><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=454856\">(2022),&nbsp;<\/a><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=454856\">no. 1,<\/a>&nbsp;Paper No. 3, 26 pp.&nbsp; &nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2101.08115\">https:\/\/arxiv.org\/abs\/2101.08115<\/a><\/li>\n\n\n\n<li>49. Classification and a priori estimate for singular prescribing Q-curvature equations on 4-manifolds. (with M. Ahmedou and Lina Wu), <strong>Journal of Functional Analysis<\/strong> 283, (2022) 109646&nbsp;<a href=\"https:\/\/people.clas.ufl.edu\/leizhang\/content-removed\/\" rel=\"attachment wp-att-569\">ahmedou-wu-zhang-jfa-22<\/a> &nbsp;,&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2012.11785\">https:\/\/arxiv.org\/abs\/2012.11785&nbsp;<\/a><\/li>\n\n\n\n<li>50. Vanishing estimates for Liouville equation with quantized singularities (with Juncheng Wei),&nbsp;<strong> Proc. London Math. Soc<\/strong>. (3) 2022;1-26&nbsp;&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2104.04988\">https:\/\/arxiv.org\/abs\/2104.04988<\/a><\/li>\n\n\n\n<li>51.Structure of bubbling solutions of Liouville systems with negative singular sources (with Yi Gu).&nbsp; <strong>Communications in Contemporary Mathematics. <span class=\"router-link-active\"><span class=\"font-weight-bold\"><a title=\"Search this volume\" data-testid=\"issue-volume\" href=\"https:\/\/mathscinet.ams.org\/mathscinet\/publications-search?query=ji%3A5306%20y%3A2026%20v%3A28\" class=\"router-link-active\">28&nbsp;<\/a><\/span><span data-testid=\"issue-year\">(<a title=\"Search this year\" href=\"https:\/\/mathscinet.ams.org\/mathscinet\/publications-search?query=ji%3A5306%20y%3A2026\" class=\"router-link-active\">2026<\/a>)<\/span><span title=\"Issue number\" data-testid=\"issue-number\">, no.&nbsp;<a title=\"Search this issue\" href=\"https:\/\/mathscinet.ams.org\/mathscinet\/publications-search?query=ji%3A5306%20y%3A2026%20v%3A28%20iss%3A3\" class=\"router-link-active\">3<\/a><\/span><span title=\"Paging\" data-testid=\"issue-paging\">, Paper No. 2550043<\/span><\/span><span data-testid=\"translated-paging-punctuation\">.<\/span> &nbsp; &nbsp;<\/strong>&nbsp; <a href=\"https:\/\/arxiv.org\/abs\/2112.10031\">https:\/\/arxiv.org\/abs\/2112.10031&nbsp;&nbsp;&nbsp;&nbsp;<\/a><\/li>\n\n\n\n<li>52. Laplacian Vanishing Theorem for Quantized Singular Liouville Equation (with Juncheng Wei).&nbsp; <strong><strong>&nbsp;J. Eur. Math. Soc. 28 (2026), no. 1, pp. 237\u2013267 &nbsp;<\/strong><\/strong><strong style=\"background-color: transparent;font-size: 13px\"><a href=\"https:\/\/doi.org\/10.4171\/jems\/1482\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"jsx-2357363445 doi\">DOI 10.4171\/JEMS\/1482<\/a><\/strong> <a style=\"background-color: transparent;font-size: 13px\" href=\"https:\/\/arxiv.org\/abs\/2202.10825\">https:\/\/arxiv.org\/abs\/2202.10825 <\/a><\/li>\n\n\n\n<li><p class=\"jsx-2357363445 cite-text\">53. Estimates of bubbling solutions of $SU(3)$ Toda systems at critical parameters-Part 2, (with Juncheng Wei and Lina Wu), <strong>Journal of London Mathematical Society<\/strong> 2 (2023), 1-47. &nbsp; &nbsp; &nbsp;http:\/\/doi.org\/10.1112\/jlms.12736.&nbsp; https:\/\/arxiv.org\/abs\/2206.08114.<\/p><\/li>\n\n\n\n<li><p class=\"jsx-2357363445 cite-text\">54. The blow-up analysis on $B_2^{(1)}$ affine Toda system: local mass and affine Weyl group (with Leilei Cui, Juncheng Wei and Wen Yang).&nbsp;<strong>&nbsp;<a data-v-3708431c=\"\" href=\"https:\/\/mathscinet.ams.org\/mathscinet\/serials\/profile?journalId=6356\" class=\"\">Int. Math. Res. Not. IMRN<\/a><span class=\"\" data-v-3708431c=\"\">(<a title=\"Search this year\" data-v-3708431c=\"\" href=\"https:\/\/mathscinet.ams.org\/mathscinet\/publications-search?query=ji%3A6356%20y%3A2023\" class=\"router-link-active\">2023<\/a>)<\/span><\/strong><span class=\"\" data-v-3708431c=\"\">, no.&nbsp;<a title=\"Search this issue\" data-v-3708431c=\"\" href=\"https:\/\/mathscinet.ams.org\/mathscinet\/publications-search?query=ji%3A6356%20iss%3A18\" class=\"router-link-active\"><span data-v-3708431c=\"\">18<\/span><\/a>, 16140\u201316199.<\/span>&nbsp; &nbsp;<a href=\"http:\/\/arxiv.org\/abs\/2206.10409\">http:\/\/arxiv.org\/abs\/2206.10409<\/a><\/p><\/li>\n\n\n\n<li>55. On Non-simple Blowup Solutions Of Liouville Equation (joint with Teresa D&#8217;Aprile and Juncheng Wei), to appear on <strong>American Journal of Mathematics<\/strong>. <a href=\"https:\/\/arxiv.org\/abs\/2209.05271\">https:\/\/arxiv.org\/abs\/2209.05271<\/a><\/li>\n\n\n\n<li>56. Non-simple blow-up for singular Liouville equation in unit ball (joint with Teresa D&#8217;Aprile and Juncheng Wei), <strong>Discrete and Continuous Dynamical Systems<\/strong>. <a href=\"https:\/\/www.aimsciences.org\/DCDS\/archive\" class=\"mainColor\">2024,&nbsp;Volume 44<\/a>,&nbsp;<a href=\"https:\/\/www.aimsciences.org\/DCDS\/article\/2024\/44\/7\" class=\"mainColor\">Issue 7<\/a>:&nbsp;1938-1957. Doi:&nbsp;<a href=\"https:\/\/doi.org\/10.3934\/dcds.2024015\" target=\"_blank\" rel=\"noopener\" class=\"mainColor\">10.3934\/dcds.2024015<\/a>&nbsp;&nbsp;<a href=\"https:\/\/people.clas.ufl.edu\/leizhang\/content-removed\/\">file:\/\/\/C:\/Users\/leizhang\/Downloads\/10.3934_dcds.2024015.pdf<\/a><\/li>\n\n\n\n<li>57. On the construction of non-simple blow-up solutions for the singular Liouville equation with a potential (joint with Teresa D&#8217;Aprile and Juncheng Wei), <strong>Calc. Var. Partial Differential Equations<\/strong> 63 (2024), no. 3, Paper No. 68.&nbsp;<a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/publications-search?query=ji%3A4611%20y%3A2024%20v%3A63%20iss%3A3\">https:\/\/mathscinet.ams.org\/mathscinet\/publications-search?query=ji%3A4611%20y%3A2024%20v%3A63%20iss%3A3<\/a> &nbsp; . <a href=\"https:\/\/arxiv.org\/abs\/2307.15811\">https:\/\/arxiv.org\/abs\/2307.15811<\/a><\/li>\n\n\n\n<li>58, Asymptotic Analysis and Uniqueness of blowup solutions of non-quantized singular mean field equations (joint with D. Bartolucci, Wen Yang),&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2401.12057\">https:\/\/arxiv.org\/abs\/2401.12057<\/a>&nbsp;  <a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/serials\/profile?journalId=734\" class=\"\">Math. Ann.<\/a><strong><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/publications-search?query=ji%3A734%20y%3A2026%20v%3A395\">&nbsp;395&nbsp;<\/a><\/strong>(<a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/publications-search?query=ji%3A734%20y%3A2026\">2026<\/a>), no.&nbsp;<a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/publications-search?query=ji%3A734%20y%3A2026%20v%3A395%20iss%3A4\">4<\/a>, Paper No. 103.<\/li>\n\n\n\n<li>59. Non degeneracy of blow-up solution]{Non degeneracy of blow-up solutions of non-quantized singular Liouville-type equations and the convexity of the mean field entropy of the Onsager vortex model with sinks (joint with Daniele Bartolucc, Wen Yang),&nbsp; to appear on <strong>Annali della Scuola Normale Superiore di Pisa, Classe di Scienze<\/strong>&nbsp; &nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2409.04664#\">https:\/\/arxiv.org\/abs\/2409.04664#<\/a><\/li>\n\n\n\n<li>60. High Order Vanishing Theorems for Nonsimple Blowup Solutions of Singular Liouville Equation&nbsp;(joint with Teresa D&#8217;Aprile, Juncheng Wei), <a href=\"https:\/\/arxiv.org\/abs\/2409.14463\">https:\/\/arxiv.org\/abs\/2409.14463<\/a>&nbsp; accepted for publication in the <strong>Transactions of the American Mathematical Society    <\/strong><a href=\"https:\/\/doi.org\/10.1090\/tran\/9742\" data-type=\"link\" data-id=\"https:\/\/doi.org\/10.1090\/tran\/9742\">https:\/\/doi.org\/10.1090\/tran\/9742<\/a>.<\/li>\n\n\n\n<li>61. Construction of Blowup Solutions for Liouville Systems (joint with Zetao Cheng and Haoyu Li),&nbsp; <strong>Proceedings of The London Mathematical Society<\/strong>. (3) 131 (2025), no. 4, Paper No. e70093. 2025. <a href=\"https:\/\/arxiv.org\/abs\/2503.07467\">https:\/\/arxiv.org\/abs\/2503.07467<\/a><\/li>\n\n\n\n<li>62.Survey on Vanishing Theorems for Liouville Equations. To appear on <strong>Contemporary Mathematics<\/strong>.<\/li>\n\n\n\n<li>63, A Learned Proximal Alternating Minimization Algorithm for a Class of Dual-Domain Nonconvex and Nonsmooth Inverse Problems Yunmei Chen, Lezhi Liu, Lei Zhang,&nbsp; <strong>Journal of Scientific Computing 103&nbsp; (2025) no. 2, Paper No. 56.<br><a href=\"https:\/\/people.clas.ufl.edu\/leizhang\/content-removed\/\" rel=\"attachment wp-att-644\">chen-liu-zhang-1<\/a>PDF&nbsp;&nbsp;<\/strong><\/li>\n\n\n\n<li>64. Long Time Existence of A Flow of Elliptic Systems ( with Woongbae Park), submitted 2025.&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2508.00551\">https:\/\/arxiv.org\/abs\/2508.00551<\/a><\/li>\n\n\n\n<li>65. Local uniqueness and non-degeneracy of blowup solutions for regular Liouville systems (with Zetao Cheng and Haoyu Li), submitted 2025.<a href=\"https:\/\/arxiv.org\/abs\/2509.09781\">https:\/\/arxiv.org\/abs\/2509.09781<\/a><\/li>\n\n\n\n<li>66. Geometric Estimates For Solutions Of Semi-linear Equations With Singular Potentials (with Thialita M. Nascimento),&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2603.00765\">https:\/\/arxiv.org\/abs\/2603.00765<\/a> &nbsp;submitted, 2026.<\/li>\n\n\n\n<li>67. Second Order Classification For Singular Liouville Equations With A Coefficient Function, with Teresa D&#8217;Aprile and Juncheng Wei. 2026.&nbsp;&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2603.11735\">https:\/\/arxiv.org\/abs\/2603.11735&nbsp;&nbsp;&nbsp;&nbsp;<\/a>&nbsp; &nbsp;submitted.<\/li>\n\n\n\n<li>68. Local Uniqueness and Non-degeneracy of Blow Up Solutions To A Chern-Simons System, with Zetao Cheng and Haoyu Li <a href=\"https:\/\/arxiv.org\/abs\/2607.01154\">https:\/\/arxiv.org\/abs\/2607.01154<\/a> , submitted. <\/li>\n\n\n\n<li>69. Non-simple blow-up for the Chern&#8211;Simons&#8211;Higgs equation: A priori analysis and constructions, with Youngae Lee. Submitted. 2026.  <a href=\"https:\/\/arxiv.org\/abs\/2609.20042\">https:\/\/arxiv.org\/abs\/2609.20042<\/a><\/li>\n\n\n\n<li>70. Isolated singularities of solutions to the Yamabe equation in higher dimensions I, with Zhengchao Han, Qingfeng Jiang, Hua-yang Wang and Jingang Xiong. 2026.  <a href=\"https:\/\/arxiv.org\/abs\/2609.28323\">https:\/\/arxiv.org\/abs\/2609.28323<\/a><\/li>\n\n\n\n<li><i><i><i><i><i>71. Liouville and Harnack Type Theorems for Semilinear Elliptic Equations and Yamabe Type Equations, PhD Thesis, Rutgers University, 2001.<\/i><\/i><\/i><\/i><\/i><\/li>\n<\/ul>\n<\/div><\/div><\/div><\/section>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":290,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-19","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/leizhang\/wp-json\/wp\/v2\/pages\/19","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/leizhang\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/leizhang\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/leizhang\/wp-json\/wp\/v2\/users\/290"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/leizhang\/wp-json\/wp\/v2\/comments?post=19"}],"version-history":[{"count":10,"href":"https:\/\/people.clas.ufl.edu\/leizhang\/wp-json\/wp\/v2\/pages\/19\/revisions"}],"predecessor-version":[{"id":750,"href":"https:\/\/people.clas.ufl.edu\/leizhang\/wp-json\/wp\/v2\/pages\/19\/revisions\/750"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/leizhang\/wp-json\/wp\/v2\/media?parent=19"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}