论文标题
与临界Allard条件的2个Varifolds的Bi-Lipschitz规律性
Bi-Lipschitz Regularity of 2-Varifolds with the Critical Allard Condition
论文作者
论文摘要
For an intergral $2$-varifold $V=\underline{v}(Σ,θ_{\ge 1})$ in the unit ball $B_1$ passing through the original point, assuming the critical Allard condition holds, that is, the area $μ_V(B_1)$ is close to the area of a unit disk and the generalized mean curvature has sufficient small $L^2$ norm, we prove $σ$是$ \ mathbb {r}^2 $本地的平面磁盘的Bi-lipschitz同型。
For an intergral $2$-varifold $V=\underline{v}(Σ,θ_{\ge 1})$ in the unit ball $B_1$ passing through the original point, assuming the critical Allard condition holds, that is, the area $μ_V(B_1)$ is close to the area of a unit disk and the generalized mean curvature has sufficient small $L^2$ norm, we prove $Σ$ is bi-Lipschitz homeomorphic to a flat disk in $\mathbb{R}^2$ locally.
