Publications



Analysis

·         Exponential growth solutions of elliptic equations (joint work with Fanghua Lin). Acta Math Sin (Engl Ser), 15 (1999) no. 4, 525-534. pdf

·         A remark on the Jacobians (joint work with Fanghua Lin). Commun Contemp Math, 2 (2000) no. 1, 35-46. pdf (modified version)

·         Topology of Sobolev mappings (joint work with Fanghua Lin). Math Res Lett, 8 (2001) no. 3, 321-330. pdf

·         Static theory for planar ferromagnets and antiferromagnets (joint work with Fanghua Lin). Acta Math Sin (Engl Ser), 17 (2001) no. 4, 541-580. pdf

·         A Liouville type theorem for minimizing maps (joint work with Fanghua Lin). Methods Appl Anal, 9 (2002), no. 3, 407-424. pdf

·         Density problems for $W^{1,1}(M,N)$. Comm Pure Appl Math, 55 (2002), no. 7, 937-947. pdf

·         Topology of Sobolev mappings II (joint work with Fanghua Lin). Acta Math, 191:1 (2003), 55-107. pdf

·         Topology of Sobolev mappings III (joint work with Fanghua Lin). Comm Pure Appl Math, 56 (2003), no. 10, 1383-1415. pdf

·         On a class of locally conformally flat manifolds (joint work with Alice Chang and Paul Yang). Int Math Res Not, 2004:4 (2004), 185-209. pdf

·         The Sobolev inequality for Paneitz operator on three manifolds (joint work with Paul Yang). Calculus of Variations and PDE, 21 (2004), no. 1, 57-83. pdf

·         On the weak limits of smooth maps for the Dirichlet energy between manifolds. Communications in Analysis and Geometry, 13 (2005), no. 5,  929-938. pdf

·         Topology of Sobolev mappings IV (joint work with Fanghua Lin). Discrete and Continuous Dynamical Systems, 13 (2005), no. 5, 1097-1124. pdf

·         Rigidity and non-rigidity results on the sphere (joint work with Xiaodong Wang). Communications in Analysis and Geometry, 14 (2006), no. 1, 91-106. pdf

·         A new approach to some nonlinear geometric equations in dimension two (joint work with Xiaodong Wang). Calculus of Variations and PDE, 26 (2006), no. 1, 119-135. pdf

·         A remark on the existence of suitable vector fields related to the dynamics of scalar semi-linear parabolic equations (joint work with Huiqiang Jiang). Proceedings of the AMS, 134 (2006), no. 9, 2633-2637. pdf

·         On the higher order conformal covariant operators on the sphere. Commun Contemp Math, 9 (2007), no. 3, 279-299. pdf

·         On a conjecture of Schroeder and Strake (joint work with Xiaodong Wang). Pacific Journal of Mathematics, 232 (2007), no. 2, 283-288. pdf

·         On the integral systems related to Hardy-Littlewood-Sobolev inequality. Math Res Lett, 14 (2007), no. 3, 373-383. pdf

·         A remark on Zhong-Yang's eigenvalue estimate (joint work with Xiaodong Wang). Int Math Res Not, 2007 (2007). pdf

·         Integral identities and Minkowski type inequalities involving Schouten tensor (joint work with  Alice Chang). Int Math Res Not, 2007 (2007). pdf

·         Sharp integral inequalities for harmonic functions (joint work with Xiaodong Wang and Xiaodong Yan). Comm Pure Appl Math, 61 (2008), no. 1, 54-95. pdf

·         An integral equation in conformal geometry (joint work with Xiaodong Wang and Xiaodong Yan). Ann H Poincare Nonl Anal, 26 (2009), no. 1, 1-21. pdf

·         Rigidity theorems for compact manifolds with boundary and positive Ricci curvature (joint work with Xiaodong Wang) Journal of Geometric Analysis, 19 (2009), no. 3, 628-642. pdf

·         Existence of Faddeev knots in general Hopf dimensions (joint work with Fanghua Lin and Yisong Yang). Surveys in differential geometry, 13 (2009), 149-221. pdf

·         Sign of Green’s function of Paneitz operators and the Q curvature (joint work with Paul Yang). International Mathematics Research Notices, 2015 (2015), no. 19, 9775-9791. pdf

·         Q curvature on a class of 3 manifolds (joint work with Paul Yang). Comm Pure Appl Math, 69 (2016), no. 4, 734-744. pdf

·         Riemannian manifolds with positive Yamabe invariant and Paneitz operator (joint work with M. Gursky and Y. J. Lin). International Mathematics Research Notices, 2016 (2016), no. 5, 1348-1367. pdf

·         Q curvature on a class of manifolds with dimension at least 5 (joint work with Paul Yang). Comm Pure Appl Math, 69 (2016), no. 8, 1452-1491. pdf

·         Lectures on the fourth order Q curvature equation (joint work with Paul Yang). Geometric Analysis Around Scalar Curvatures, 1-33, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., 31, World Sci. Publ., Hackensack, NJ (2016). pdf

·         Paneitz operator for metrics near S³ (joint work with Paul Yang). Calc. Var. Partial Differential Equations 56 (2017), no. 4, Art. 106, 26 pp. pdf

·         A perturbation approach for Paneitz energy on standard three sphere (joint work with Paul Yang). International Mathematics Research Notices, 2020 (2020), no. 11, 3295-3317. pdf

·         The sphere covering inequality and its dual (joint work with Changfeng Gui and Amir Moradifam). Comm Pure Appl Math, 73 (2020), no. 12, 2685-2707. pdf

·         Remarks on a mean field equation on S2 (joint work with Changfeng Gui, Amir Moradifam and Xiaodong Wang). Journal of Mathematical Study, special issue for 70th birthdays of Professor Alice Chang and Paul Yang, 54 (2021), no. 1, 81-88. pdf

·         Liouville type theorems on manifolds with nonnegative curvature and strictly convex boundary (joint work with Qianqiao Guo and Xiaodong Wang).  Math Res Lett, to appear. pdf

·         Improved Moser-Trudinger-Onofri inequality under constraints (joint work with Alice Chang). Comm Pure Appl Math, 75 (2022), no. 1, 197-220.  pdf

·         A remark on the concentration compactness principle in critical dimension. Comm Pure Appl Math, to appear. pdf

·         Improved Sobolev inequality under constraints (joint work with Xiaodong Wang). International Mathematics Research Notices, to appear. pdf

·         Aubin type almost sharp Moser-Trudinger inequality revisited. Journal of Geometric Analysis, to appear. pdf


Numerical Analysis  

·         Lattice sums and the two-dimensional, periodic Green's function for the Helmholtz equation (joint work with  A. Dienstfrey and  Jingfang Huang).  R Soc Lond Proc Ser A  Math Phys Eng Sci, 457 (2001) no. 2005, 67-85. pdf

·         On applicability of the sparse grid method in the worst case setting (joint work with Youming Li). Numerical Algorithms, 42 (2006), no. 2, 95-105.  pdf

·         Generalized Poincare-Betrand formula on a hypersurface (joint work with Shidong Jiang). Applied and computational harmonic analysis, 27 (2009), no. 1, 100-116. pdf

 


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