The Bernstein theorem for a class of fourth order equations
Bin Zhou
ANU
Abstract
In this talk, we concern on a class of fourth order equations of Monge-Ampere type. In particular, affine maximal surface equation from affine geometry and Abreu's equation arising from scalar curvature equation on toric Kahler manifolds are included. I will talk about the 2-dimensional Bernstein theorem for these equations, i.e., the entire solution to these equations must be quadratic polynomials. The main ingredients are interior estimates and the proof of strict convexity for the solutions.