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# Geometric Analysis and Partial Differential Equations Seminar

## April 10, 2013 @ 10:30 am - 11:30 pm

##### Speaker

Dr Bin Zhou (Australian National University)

##### Title

The Bernstein theorem for a class of fourth order equations

##### 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.