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

2016/07/28 by Miquel, Vicente, Viñado-Lereu, Francisco
#35R01 #53C44 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.08402

Abstract

We define Type I singularities for the mean curvature flow associated to a density ψ (ψMCF) 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 ψ-curvature due to the density. We describe a family of curves whose evolution under ψMCF (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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