Singularities of mean convex level set flow in general ambient manifolds

Robert Haslhofer; Or Hershkovits

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arXiv · 1508.00840

Singularities of mean convex level set flow in general ambient manifolds

Robert Haslhofer·Or Hershkovits

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Abstract

We prove two new estimates for the level set flow of mean convex domains in Riemannian manifolds. Our estimates give control - exponential in time - for the infimum of the mean curvature, and the ratio between the norm of the second fundamental form and the mean curvature. In particular, the estimates remove a stumbling block that has been left after the work of White and Haslhofer-Kleiner, and thus allow us to extend the structure theory for mean convex level set flow to general ambient manifolds of arbitrary dimension.

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Robert Haslhofer, Or Hershkovits. 2015-08-04. Singularities of mean convex level set flow in general ambient manifolds. https://arxiv.org/abs/1508.00840

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