Host：Dr. Liding Huang
Speaker：Dr. Bin Zhou, Peking Univerity
Time：14:00-15:00, Tuesday, June 14th, 2022
Venue：ZOOM
Biography：
Dr. Bin Zhou, an Associate Professor of the School of Mathematical Sciences, Peking University. He graduated from Peking University and the Australian National University in 2010. His research interests are complex geometry, geometric analysis and fully nonlinear equations. His work has been published in Adv. Math.; JFA; CVPDE; JDE and other famous journals.
Abstract：
In this talk, we give several new approaches to study the interior estimates for a class of fourth order equations of Monge-Amp`ere type. First, we prove the interior estimates for the homogeneous equation in dimension two by using the partial Legendre transform. As an application, we obtain a new proof of the Bernstein theorem without using Caffarelli-Guti ́errez's estimate, including the Chern conjecture on the affine maximal surfaces. For the inhomogeneous equation, we also obtain a new proof in dimension two by an integral method relying on the Monge-Amp`ere Sobolev inequality. This proof works even when the right hand side is singular. In higher dimensions, we obtain the interior regularity in terms of the integral bounds on the second derivatives and the inverse of the determinant.
ZOOM ID：872 2965 2390
PASSCODE：396259
