MINIMAL GRAPHS OF ARBITRARY CODIMENSION IN EUCLIDEAN SPACE

讲座时间 Datetime: 2022年6月23日，星期四，  15:00-16:00

地点 Venue: 腾讯线上会议：926252265

 主持人 Host：魏国栋

报告人 Speaker:丁琪

单位 Affiliation:上海数学中心

报告摘要 Abstract:

Codimension 1 minimal graphs in Euclidean space have been studied suc- cessfully by many mathematicians, while minimal graphs of high codimension have many differences from the situation of codimension 1, and are far away from a thorough understanding.

For a locally Lipschitz map f : Rn → Rm, f is said to have 2-dilation ≤ Λ for some constant Λ ≥ 0 if vol(f(S)) ≤ Λvol(S) for each 2-dimensional Borel set S ⊂ Rn. Let M(n,Λ) denote a space containing all locally Lipschitz minimal graphs of dimension n and of arbitrary codimension m in Rn+m with uniformly bounded 2-dilation Λ of their graphic functions. In this talk, we will discuss how this is a natural class to extend structural results known for codimension one. As applications, we get Liouville’s theorem and Bernstein theorem. This work is joint with J. Jost and Y.L. Xin.