On the Convergence of Axially Symmetric Volume Preserving Mean Curvature Flow

Maria Athanassenas; Sevvandi Kandanaarachchi

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arXiv · 1108.5849

On the Convergence of Axially Symmetric Volume Preserving Mean Curvature Flow

Maria Athanassenas·Sevvandi Kandanaarachchi

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Abstract

We study the convergence of an axially symmetric hypersurface evolving by volume preserving mean curvature flow. Assuming the surface is not pinching off along the axis at any time during the flow, and without any additional conditions, as for example on the curvature, we prove that it converges to a hemisphere, when the hypersurface has a free boundary and satisfies Neumann boundary data, and to a sphere when it is compact without boundary.

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BibTeX RIS

Maria Athanassenas, Sevvandi Kandanaarachchi. 2011-08-30. On the Convergence of Axially Symmetric Volume Preserving Mean Curvature Flow. https://arxiv.org/abs/1108.5849

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