On the extension of axially symmetric volume flow and mean curvature flow

John Head; Sevvandi Kandanaarachchi

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arXiv · 1301.1125

On the extension of axially symmetric volume flow and mean curvature flow

John Head·Sevvandi Kandanaarachchi

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Abstract

We study the provenance of singularity formation under mean curvature flow and volume preserving mean curvature flow in an axially symmetric setting. We prove that if the mean curvature is uniformly bounded on any finite time interval, then no singularities can develop during that time under both mean curvature flow and volume preserving mean curvature flow.

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John Head, Sevvandi Kandanaarachchi. 2013-01-07. On the extension of axially symmetric volume flow and mean curvature flow. https://arxiv.org/abs/1301.1125

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