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), preprint.

Convex solutions to the mean curvature flow, preprint.

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

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

On the reflector shape design (with Aram Karakhanyan), J. Diff. Geom., 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, Springer, 2009, 70pp.

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, Inter. Press, 2008, pp. 467-524.

Boundary regularity for the Monge-Ampère 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.