An-Min Li

The Calabi Conjecture on Affine Maximal Surfaces

There are different versions of so called affine Bernstein conjectures, stated by Calabi and Chern, resp. In [T-W] the authors present a proof of Chern’s conjecture. In this paper we give an affirmative answer to Calabi’s conjecture.

Cubic Form Methods and Relative Tchebychev Hypersurfaces

We introduce the concept of a relative Tchebychev hypersurface which extends that of affine spheres in equiaffine geometry and also that of centroaffine Tchebychev hypersurfaces and give partial local and global classifications for this new class. Our tools concern a new operator and interesting properties of the traceless part of the cubic form.

Hypersurfaces with Prescribed Affine Gauss–Kronecker Curvature

We extend a procedure for solving particular fourth order PDEs by splitting them into two linked second order Monge–Ampère equations. We use this for the global study of Blaschke hypersurfaces with prescribed Gauss–Kronecker curvature.

Differential inequalities on homogeneous toric bundles

We study the generalized Abreu equation in n-dimensional polytopes and derive some differential inequalities for homogeneous toric bundles.