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.