AFFINE MAXIMAL HYPERSURFACES

This is a brief survey of recent works by Neil Trudinger and myself on the Bernstein problem and Plateau problem for affine maximal hypersurfaces.

[1]  Kurt Leichtweiss,et al.  Affine geometry of convex bodies , 1998 .

[2]  S. Yau,et al.  Complete affine hypersurfaces. Part I. The completeness of affine metrics , 1986 .

[3]  H. W. Turnbull,et al.  Vorlesungen uber Differential Geometrie , 1909, The Mathematical Gazette.

[4]  K. Jörgens Über die Lösungen der Differentialgleichungrt−s2=1 , 1954 .

[5]  An-Min Li,et al.  The Calabi Conjecture on Affine Maximal Surfaces , 2001 .

[6]  L. Caffarelli Interior $W^{2,p}$ estimates for solutions of the Monge-Ampère equation , 1990 .

[7]  N. Trudinger,et al.  On locally convex hypersurfaces with boundary , 2002 .

[8]  C. E. Gutiérrez,et al.  Properties of the solutions of the linearized Monge-Ampère equation , 1997 .

[9]  N. Trudinger,et al.  Affine complete locally convex hypersurfaces , 2002 .

[10]  Eugenio Calabi,et al.  Hypersurfaces with Maximal Affinely Invariant Area , 1982 .

[11]  Joel Spruck,et al.  Boundary-value problems on $\mathbb{S}^n$ for surfaces of constant Gauss curvature , 1993 .

[12]  E. Lutwak Extended affine surface area , 1991 .

[13]  N. Trudinger,et al.  The Bernstein problem for affine maximal hypersurfaces , 2000 .

[14]  Fully Nonlinear Elliptic Equations and Applications to Geometry , 1995 .

[15]  E. Calabi Affine differential geometry and holomorphic curves , 1990 .

[16]  Xu-jia Wang,et al.  Interior curvature bounds for a class of curvature equations , 2004 .

[17]  Su Buqing,et al.  Affine differential geometry , 1983 .