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arXiv · 1806.00930

Asymptotics for the level set equation near a maximum

Nick Strehlke
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Abstract

We give asymptotics for the level set equation for mean curvature flow on a convex domain near the point where it attains a maximum. It is known that solutions are not necessarily $C^3,$ and we recover this result and construct non-smooth solutions which are $C^3.$ We also construct solutions having prescribed behavior near the maximum. We do this by analyzing the asymptotics for rescaled mean curvature flow converging to a stationary sphere.

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Nick Strehlke. 2018-06-04. Asymptotics for the level set equation near a maximum. https://arxiv.org/abs/1806.00930

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