论文标题
varifolds自由边界的可纠正性
Rectifiability of the free boundary for varifolds
论文作者
论文摘要
我们为$ k $ -Varifold $ v $的自由边界建立了部分可重差结果。也就是说，我们首先通过表明具有自由边界的通用varifold的第一个变化是ra尺度来完善格吕特和乔斯特定理。接下来，我们表明，如果$ v $的平均曲率$ h $在[1，k] $中的$ l^p $中是$ l^p $，那么最多$ k-p $的$ k $ v $ $ k $ - 密度不存在或Infinite具有Hausdorff dimension的点集。我们使用此结果来证明，在适当的假设下，$ v $的第一个变化的一部分具有正和有限$（k-1）$ - 密度为$（k-1）$ - 可重新合转。
We establish a partial rectifiability result for the free boundary of a $k$-varifold $V$. Namely, we first refine a theorem of Grüter and Jost by showing that the first variation of a general varifold with free boundary is a Radon measure. Next we show that if the mean curvature $H$ of $V$ is in $L^p$ for some $p \in [1,k]$, then the set of points where the $k$-density of $V$ does not exist or is infinite has Hausdorff dimension at most $k-p$. We use this result to prove, under suitable assumptions, that the part of the first variation of $V$ with positive and finite $(k-1)$-density is $(k-1)$-rectifiable.
