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arXiv · 1307.0423

Singularities of mean curvature flow and isoperimetric inequalities in H^3

Kui Wang
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Abstract

In this article, by following the method in \cite{PT}, combining Willmore energy with isoperimetric inequalities, we construct two examples of singularities under mean curvature flow in $\mathbb{H}^3$. More precisely, there exists a torus, which must develop a singularity under MCF before the volume it encloses decreases to zero. There also exists a topological sphere in the shape of a dumbbell, which must develop a singularity in the flow before its area shrinks to zero. Simultaneously, by using the flow, we proved an isoperimetric inequality for some domains in $\mathbb{H}^3$.

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Kui Wang. 2013-07-02. Singularities of mean curvature flow and isoperimetric inequalities in H^3. https://arxiv.org/abs/1307.0423

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