More publications

Recent papers

  • The intermediate case of the Yamabe problem for higher order curvatures, (with N.S. Trudinger), preprint.

  • Moser-Trudinger type inequalities for the k-Hessian equation (with Guji Tian), preprint.

  • Interior C^{2, alpha} estimate for potential functions in optimal transportation, (with Jiakun Liu, N.S. Trudinger), Comm. PDEs, to appear.

  • Convex solutions to the mean curvature flow, preprint.

  • The mean curvature measure, (with Qiuyi Dai, N.S. Trudinger), preprint.

  • On the reflector shape design (with Aram Karakhanyan), J. Diff. Geom., to appear.

  • Singularity profile in the mean curvature flow (with W.M. Sheng), Methods and Applications of Analysis, to appear.

  • On strict convexity and C^1 regularity of potential functions in optimal transportation, (with N.S. Trudinger), Arch. Rat. Mech. Anal., 192(2009), 403-418.

  • Quasilinear elliptic equations with signed measure data (with N.S. Trudinger), Discrete and Continuous Dynamical Systems, 23(2009), 477--494.

  • On the second boundary value problem for Monge-Ampere type equations and optimal transportation (with NS Trudinger), Ann. Scuola Norm. Sup. Pisa, 8(2009), 1-32.

  • The k-Hessian equation, Lectures Notes in Mathematics, Vol.1977, 2009, pp.177-252.

  • On Harnack inequalities and singularities of admissible metrics in the Yamabe problem, (with N.S. Trudinger), Calc. Var. PDE, 35(2009), 317-338.

  • A class of Sobolev type inequalities (with Guji Tian), Methods and Applications of Analysis, 15(2008), 257-270.

  • The Monge-Ampere equation and its geometric applications (with N.S. Trudinger), Handbook of Geometric Analysis, 2008, pp. 467-524.

  • Boundary regularity for the Monge-Ampere and affine maximal surface equations, (with N.S. Trudinger), Ann. Math., 167(2008), 993-1028.

  • Continuity estimates for the Monge-Ampere equation, (with Huaiyu Jian), SIAM J Math Anal, 39(2007), 608-626..

  • The Yamabe problem for higher order curvatures, (with W.M. Sheng and N.S. Trudinger), J. Diff. Geom. 77(2007), 515-553.

  • Schauder estimates for elliptic and parabolic equations, Chinese Ann. Math., 27(2006), 637-642.

  • The L^p Minkowski problem, (with K.S. Chou), Adv. Math., 205 (2006), 33--83.

  • A priori estimates and existence for a class of fully nonlinear elliptic equations in conformal geometry, Chinese Ann. Math., 27(B) (2006), 169-178.

    • Some previous publications

  • Regularity of potential functions of the optimal transportation problem, (with X.Ma and N.Trudinger), Arch. Rat. Mech. Anal., 177(2005), 151-183.

  • The affine Plateau problem, (with N. Trudinger), J. Amer. Math. Soc., 18 (2005), 253-289.

  • Kahler-Ricci solitons on toric manifolds with positive first Chern class (with X.H. Zhu), Advances in Math., 188(2004), 87-103.

  • Interior curvature bounds for a class of curvature equations (with W.M. Sheng and J. Urbas), Duke Math J. 123(2004), 235--264

  • On the design of a reflector antenna II, Calc. Var. PDE, 20(2004), 329-341.

  • Affine maximal hypersurfaces, Proc. Inter. Congress Math. Vol. III (Beijing, 2002), 221--231.

  • Locally convex hypersurfaces with boundary, (with N.S. Trudinger), J. reine angew. Math., 551(2002), 11-32.

  • Affine complete locally convex hypersurfaces, (with N.S. Trudinger), Invent. Math., 150(2002), 45-60.

  • On the weak continuity of elliptic operators and applications to potential theory (with N.S. Trudinger), Amer. J. Math., 124 (2002), 369-410.

  • On Monge's mass transfer problem (with N.S. Trudinger) , Calc. Var. PDE, 13(2001), 19-31.

  • A variational theory of the Hessian equation (with K.S. Chou), Comm. Pure Appl. Math., 54(2001), 1029-1064.

  • The logarithmic Gauss curvature flow (with K.S. Chou), Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 17(2000), 733-751.

  • The Bernstein problem for affine maximal hypersurfaces (with N.S. Trudinger) , Invent. Math., 140(2000), 399-422.

  • Hessian Measures II, (with N.S. Trudinger), Ann. of Math. 150 (1999), 579--604.

  • On the Dirichlet problem for degenerate Monge-Ampère equations (with P.Guan and N.S. Trudinger), Acta Math., 182(1999), 87-104.

  • Interior gradient estimates for mean curvature equations, Math. Zeitschrift, 228(1998), 73-81.

  • Existence of convex hypersurfaces with prescribed Gauss-Kronecker curvature, Trans. Amer. Math. Soc., 348(1996), 4501-4524.

  • Entire solutions of the Monge-Ampère equation (with K.S. Chou), Comm. Pure Appl. Math., 49(1996), 529-539.

  • On the design of a reflector antenna, Inverse Problems, 12(1996), 351-375.

  • A class of fully nonlinear elliptic equations and related functionals, Indiana Univ. Math. J. 43 (1994), 25--54.

  • Neumann problems of semilinear elliptic equations involving critical Sobolev exponents, J. Differential Equations, 93(1991), 283--310.

    • See also www.ams.org
    Last modified: March 22, 2006