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arXiv · 1607.08402

Type I singularities in the curve shortening flow associated to a density

Vicente Miquel·Francisco Viñado-Lereu
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Abstract

We define Type I singularities for the mean curvature flow associated to a density $\psi$ ($\psi$MCF) and describe the blow-up at singular time of these singularities. Special attention is paid to the case where the singularity come from the part of the $\psi$-curvature due to the density. We describe a family of curves whose evolution under $\psi$MCF (in a Riemannian surface of non-negative curvature with a density which is singular at a geodesic of the surface) produces only type I singularities and study the limits of their blow-ups.

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Vicente Miquel, Francisco Viñado-Lereu. 2016-07-28. Type I singularities in the curve shortening flow associated to a density. https://arxiv.org/abs/1607.08402

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