几何分析讨论班

报告题目：Bi-Lipschitz regularity of 2-varifolds with the critical Allard condition

报 告 人：周杰 教授（首都师范大学）

时  间：2026年10月19日（星期一），上午10:30-11:30

地  点：海纳苑2幢203

摘  要：Let V=v(M,θ≥1) be an n dimensional rectifiable varifold. The classical  Allard regularity says, if  the mass  μ_V(B_1) is close to the volume of n dimensional unit ball and the generalized mean curvature has small L^p norm for super critical p>n, then M is a C^{1,α} graph for α=1-n/p.  In this talk, we discuss the two dimensional critical case, that is, for an integral 2-varifold V =v(Σ,θ)  in the unit ball  B_1 such that 0∈Σ and θ≥1, assuming that the critical  Allard condition holds; namely, μ_V(B_1) is close to the area of the unit disk and the generalized mean curvature has  sufficiently small L^2-norm, we prove that Σ is locally bi Lipschitz homeomorphic to a flat disk in R^2. This is a joint work with Yuchen Bi at the University of Freiburg.