Regularity of the level set flow

2016/06/16 by Tobias Holck Colding, Colding, Tobias Holck, William P. Minicozzi II +1
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.1606.05185

arxiv created 2016/06/16 · arxiv updated 2016/06/17

Abstract

We showed earlier that the level set function of a monotonic advancing front is twice differentiable everywhere with bounded second derivative. We show here that the second derivative is continuous if and only if the flow has a single singular time where it becomes extinct and the singular set consists of a closed C¹ manifold with cylindrical singularities.

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