# Publications

• 1.Classification of conformal metrics on $R^2_+$ with constant Gauss curvature and geodesic curvature on the boundary under various integral finiteness assumptions, Calc. Var. Partial Differential Equations, 16, (2003), no.4, 405-430.
• 2. Refined Asymptotic Estimates for Conformal Scalar Curvature Equation Via Moving Sphere Method, J. Functional Analysis, 192, (2002), no.2, 491-516.
• 3. Arbitrarily Large Solutions of the Scalar Curvature Equation at an Isolated Singularity (with S.Taliaferro), Proc. Amer. Math. Soc, 131 (2003), no.9, 2985-2902.
• 4. Liouville type theorems and Harnack type inequalities for semi-linear elliptic equations (with Y.Y. Li), J. Anal. Math, 90(2003), 27-87.
• 5. A Harnack type inequality for the Yamabe equation in low dimensions (with Y. Y. Li), Calc. Var. Partial Differential Equations 20 (2004), 133-151.
• 6. Compactness of solutions to the Yamabe problem (with Y. Y. Li), C. R. Acad. Sci. Paris, Ser. I 338 (2004), 693-695.
• 7. Compactness of solutions to the Yamabe problem II (with Y. Y. Li), Calc. Var. Partial Differential Equations, 24 (2005), no. 2, 185–237.
• 8. A priori estimates and uniqueness results for some mean-field equation, (with M. Lucia), J. Differential Equations, 217 (2005), no. 1, 154–178.
• 9. Asymptotic symmetry for conformal scalar curvature equation with singularities (with S.Taliaferro). Calc. Var. Partial Differential Equations, 26, (2006) no 4: 401-428.
• 10. Blowup solutions for some nonlinear elliptic equations involving exponential nonlinearities, Comm. Math. Phys, 268, (2006) no 1: 105-133.
• 11. Compactness of solutions to the Yamabe problem III (with Y. Y. Li). J. Functional Analysis, 245 (2007) 438-474.
• 12. Harnack Type Inequalities for conformal scalar curvature equation, Math. Ann, (2007) 339, 195-220.
• 13. Prescribing curvatures on three dimensional Riemannian manifolds with boundaries, Trans. Amer. Math. Soc. 361 (2009), 3463-3481.
• 14. Asymptotic behavior of blowup solutions for elliptic equations with exponential nonlinearity and singular data, Communications in Contemporary  mathematics, vol 11, issue 3, June 2009, 395-411. Also available at arXiv:0810.5143.
• 15. A priori estimate for a family of semi-linear elliptic equations with critical nonlinearity, Journal of Differential Equations, 247 (2009) 1334-1353, also available at arXiv:0810.5140
• 16. The profile of bubbling solutions of a class of fourth order geometric equations on 4-manifolds, (with G. Weinstein), Journal of Functional Analysis, Volume 257 (2009), Issue 12, 3895-3929, available at arXiv: 0810.4879
• 17. Profile of bubbling solutions to a Liouville system (with Chang-shou Lin), Annales de l’Institut Henri Poincare / Analyse non lineaire, Volume 27, Issue 1, January-February 2010, Pages 117-143, available at arxiv 0903.0381:
• 18. The monotonicity theorems for the Laplace-Beltrami operator, (with E. Teixeira), Advances in Mathematics, Vol. 226, Issue 2, 30 January 2011, pp. 1259-1284.
• 19. A local parabolic monotonicity formula on Riemannian manifolds (with E. Teixeira), Journal of Geometric Analysis: Volume 21, Issue 3 (2011), Page 513-526, available at arxiv 0906.1483:
• 20. A topological degree counting for some Liouville systems of mean field equations (with Chang-shou Lin), Comm. Pure Appl. Math. volume 64, Issue 4, pages 556–590, April 2011.
• 21. An elliptic variational problem involving level surface area on Riemannian manifolds (with E. Teixeira), Revista Matematica Iberoamericana 28 (2012), no. 3, 759–772.
• 22. Local gradient estimate for p-harmonic functions on Riemannian manifolds (with X. Wang ), Comm. Anal. Geom, volume 19 (2011), no 4, 759-772, also available at arxiv 1010.2889.
• 23. Monge-Ampere equations on exterior domains (with Jiguang Bao, Haigang Li ), Cal. Var. PDE.52 (2015), no. 1-2, 39–63. , arxiv: 1304:2415 http://arxiv.org/abs/1304.2415
• 24. On Liouville systems at critical parameters, Part 1: One bubble. (with Chang-shou Lin), Journal of Functional Analysis vol. 264 (2013) 2584-2636, arxiv: 1302.1147.
• 25. Classification of blowup limits for SU(3) singular Toda systems (with Chang-shou Lin and Juncheng Wei), Analysis and PDE, Vol. 8 (2015), No. 4, 807–837. , arxiv:1303:4167  http://arxiv.org/abs/1303.4167
• 26. Classification of Radial Solutions to Liouville Systems with Singularities (with Chang-shou Lin), DCDS-A, Volume 34, Issue 6, June 2014, Pages: 2617 – 2637 arxiv: 1302:3866.lin-zhang-dcds-a
• 27. Local profile of fully bubbling solutions to SU(n+1) Toda systems (with Chang-shou Lin and Juncheng Wei), Journal of European Mathematical Society, vol 18, issue 8, 1707-1728, 2016.  arxiv: 1308.1579 http://arxiv.org/abs/1308.1579
• 28. A Harnack-Type Inequality for a Prescribing Curvature equation on a Domain with Boundary (with Mathew Gluck and Ying Guo),  Adv. Nonlinear Stud. 14 (2014), no. 3, 709–746. arxiv: 1309.1135. bry-harnack-gluck-guo
• 29. Energy estimates for a class of semilinear elliptic equations on half Euclidean balls (with Ying Guo),  Revista Matematica Iberoamericana, vol 31, issue 4, 2015, 1141-1166.  arxiv: 1309.5081 . guo-zhang
• 30. Blowup solutions of elliptic systems in two dimensional spaces. Proceedings of the Sixth International Congress of Chinese Mathematicians. Vol. II, 617–624, Adv. Lect. Math. (ALM), 37, Int. Press, Somerville, MA, 2017. arxiv: 1311.0694.
• 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),  Advances in Mathematics. v 285, 5,  November 2015, Pages 1189–1224  arxiv: 1410.7410  http://arxiv.org/abs/1410.7410
• 32. Classification of solutions to a critically nonlinear system of elliptic equations on Euclidean half-space, (with Mathew Gluck), J. Part. Diff. Eq., 28 (2015), pp. 74-94.
• 33. Global Monge-Ampere equations with asymptotically periodic data (with Eduardo Teixeira), Indiana Univ. Math. J. 65 No. 2 (2016), 399–422. arxiv: 1406.1386. http://arxiv.org/abs/1406.1386
• 34. Vanishing estimates for fully bubbling solutions of $SU(n+1)$ Toda Systems at a singular source,   International mathematics research notices.Volume 2020, Issue 18, September 2020, Pages 5774–5795, https://doi.org/10.1093/imrn/rny183  it can also be found at .https://arxiv.org/abs/1804.07685.
• 35. Energy concentration for Singular $B_2$ and $G_2$ Toda systems (with Chang-shou Lin), Int Math Res Notices . 2016, No. 16, pp. 5076–5105 ..http://arxiv.org/abs/1505.03012
• 36. Global solutions and exterior Dirichlet problem for Monge-Ampere equations in $\mathbb R^2$ (with J. G. Bao and H. G. Li ) ,  Differential Integral Equations 29 (2016), no. 5-6, 563–582.
• 37. Optimal $C^{1,\alpha}$ estimates for a class of elliptic quasilinear equations (with Damiao Araujo), http://arxiv.org/abs/1507.06898  Commun. Contemp. Math. 22 (2020), no. 5, 1950014, 19 pp
• 38. The domain geometry and the bubbling phenomenon of rank two Gauge theory (with Hsin-Yuan Huang). http://arxiv.org/abs/1510.07055  Comm. Math. Phys. 349 (2017), no. 1, 393–424.
• 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). Analysis & PDE vol 11, no 4. (2018) 873–898  http://arxiv.org/abs/1609.02772
• 40. Degree counting for Toda system with simple singularity: One point blow up, (with Youngae Lee, Chang-shou Lin, Wen Yang), J. Differential Equations 268 (2020), no. 5, 2163–2209.   .http://arxiv.org/abs/1707.07156
• 41.Non-degeneracy of Gauss curvature equation with negative conic singularity (with Juncheng Wei). Pacific Journal of Mathematics 297-2 (2018), 455–475. DOI 10.2140/pjm.2018.297.455.   https://arxiv.org/abs/1706.10264
• 42. Degree counting theorems for singular Liouville systems ( with Yi Gu)  Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)
Vol. XXI (2020), 1103-1135. also available at https://arxiv.org/abs/1811.00190
• 43. Estimates for Liouville equation with quantized singularities, with Juncheng Wei, Advances in Mathematics, 380 (2021), 107606.
• 44. Uniqueness of bubbling solutions of mean field equations with non-quantized singularities, with Lina Wu, Commun. Contemp. Math. 23 (2021), no. 4, 2050038, 39 pp.   https://arxiv.org/abs/1906.05914.
• 45. Estimates of bubbling solutions of $SU(3)$ Toda systems at critical parameters-part 1 (with Lina Wu), SIAM J. Math. Anal. 52 (2020), no. 4, 3738–3776. https://arxiv.org/abs/1912.12071
• 46.  Isolated singularities of solutions to the Yamabe equation in dimension 6 (with Jingang Xiong), to appear on international mathematics research noticeshttps://arxiv.org/abs/2006.13279
• 47. Yamabe equation on exteiror domains (with Zhengchao Han and Jingang Xiong), coming up shortly.
• 48. On Liouville systems at critical parameters, Part II: Multiple bubbles (with Hsin-Yuan Huang), submitted.  https://arxiv.org/abs/2101.08115
• 49. Classification and a priori estimate for singular prescribing Q-curvature equations on 4-manifolds. (with M. Ahmedou and Lina Wu), submitted, https://arxiv.org/abs/2012.11785
• 50. Vanishing estimates for Liouville equation with quantized singularities (with Juncheng Wei), submitted, 2021.  https://arxiv.org/abs/2104.04988
• 51. Liouville and Harnack Type Theorems for Semilinear Elliptic Equations and Yamabe Type Equations, PhD Thesis, Rutgers University, 2001.