中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

 

报告人:周杰 (首都师范大学)

  Critical Allard regularity in dimension two and its application

  2022.12.01(星期四)14:00-15:00

 点:腾讯会议:936-2656-1072

  要:The classical Allard regularity says, a rectifiable varifold in the unit ball of the Euclidean space passing through the original point with volume density close to 1 and generalized mean curvature small in $L^p$ for some super-critical $p>n$ must be a C^{1,\alpha=1-n/p} graph with estimate. In this presentation, we discuss the critical case $p=n=2$ in two dimensional case. We get the bi-Lipschitz regularity and apply it to analysis the quantitative rigidity for $L^2$ almost CMC surfaces in $R^3$. This is a joint work with Yuchen Bi.

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