主持人：黄立鼎博士
主讲人：北京大学 周斌博士
时间：2022年6月14日（星期二）14:00-15:00
地点：ZOOM
主讲人简介：
周斌博士，2010年毕业于北京大学和澳大利亚国立大学，现北京大学数学学院副教授。主要从事复几何，几何分析和完全非线性方程的研究，系列工作发表在 Adv. Math.、JFA、CVPDE、JDE等数学领域著名期刊上。2012年获得澳大利亚基金会Discovery Early Career Research Award奖，2018年获得国家优秀青年基金资助。
报告摘要：
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会议号：872 2965 2390
密码：396259
