A revisit to the affine Bernstein theorem

Date: 2021-04-16 14:00:00
Time: 14:00-15:00
Venue: Yuquan Campus
Speaker: ZHOU Bin
Category: Talk & Lecture

Speaker: ZHOU Bin, Associate Professor of Peking University

Venue: Room 200-9, Sir Run Run Shaw Business Administration Building, Yuquan Campus


In this talk, I will first review the Bernstein theorem for a class of fourth order equations of Monge-Ampere type, including the affine maximal surface equation and Abreu’s equation. The famous affine Bernstein theorem, also called Chern’s conjecture, was first proved by Trudinger-Wang in dimension two in 2000. Then I will present a new proof without using Caffarelli-Gutierrez’s regularity for the linearized Monge-Ampere equation. The new idea is to establish the interior estimates of the fourth order equations by partial Legendre transform.