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arXiv · 1911.01186

Mean convex mean curvature flow with free boundary

Nick Edelen·Robert Haslhofer·Mohammad N. Ivaki·Jonathan J. Zhu
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Abstract

In this paper, we generalize White's regularity and structure theory for mean-convex mean curvature flow to the setting with free boundary. A major new challenge in the free boundary setting is to derive an a priori bound for the ratio between the norm of the second fundamental form and the mean curvature. We establish such a bound via the maximum principle for a triple-approximation scheme, which combines ideas from Edelen, Haslhofer-Hershkovits, and Volkmann. Other important new ingredients are a Bernstein-type theorem and a sheeting theorem for low entropy free boundary flows in a halfslab, which allow us to rule out multiplicity 2 (half-)planes as possible tangent flows and, for mean convex domains, as possible limit flows.

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Nick Edelen, Robert Haslhofer, Mohammad N. Ivaki, Jonathan J. Zhu. 2019-11-04. Mean convex mean curvature flow with free boundary. https://doi.org/10.1002/cpa.22009

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