论文标题
平坦奇异点最小表面的动力不稳定性
Dynamical instability of minimal surfaces at flat singular points
论文作者
论文摘要
假设一个可计数的$ n $ -rectifiable集合$γ_0$是$ \ mathbb {r}^{n+1} $中的多重性 - 一个固定的varifold，并且可以承认一个平坦的切线平面$ t $ t $ t $ t $ t $ os $ q \ egeq 2 $。我们证明，根据$γ_0$ $ t $的爆炸率的适当假设，存在以$γ_0$开头的非恒定brakke流。这表明在这些条件下Brakke流的非唯一性，并表明可以使用固定的Varifold相对于平均曲率流的稳定性来排除平面奇异性的存在。
Suppose that a countably $n$-rectifiable set $Γ_0$ is the support of a multiplicity-one stationary varifold in $\mathbb{R}^{n+1}$ with a point admitting a flat tangent plane $T$ of density $Q \geq 2$. We prove that, under a suitable assumption on the decay rate of the blow-ups of $Γ_0$ towards $T$, there exists a non-constant Brakke flow starting with $Γ_0$. This shows non-uniqueness of Brakke flow under these conditions, and suggests that the stability of a stationary varifold with respect to mean curvature flow may be used to exclude the presence of flat singularities.
