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Mathematics > Analysis of PDEs
Title: Dynamical instability of minimal surfaces at flat singular points
(Submitted on 31 Aug 2020 (v1), last revised 7 May 2024 (this version, v2))
Abstract: Suppose that a countably $n$-rectifiable set $\Gamma_0$ 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 $\Gamma_0$ towards $T$, there exists a non-constant Brakke flow starting with $\Gamma_0$. 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.
Submission history
From: Salvatore Stuvard [view email][v1] Mon, 31 Aug 2020 16:45:15 GMT (315kb,D)
[v2] Tue, 7 May 2024 11:58:43 GMT (393kb,D)
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