Data di Pubblicazione:
2020
Citazione:
Dynamical instability of minimal surfaces at flat singular points / S. Stuvard, Y. Tonegawa. - (2020 Aug 31).
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 $Q≥2$. 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.
Tipologia IRIS:
24 - Pre-print
Keywords:
mean curvature flow; varifolds; singularities of minimal surfaces
Elenco autori:
S. Stuvard, Y. Tonegawa
Link alla scheda completa:
Link al Full Text: