The level set flow of a hypersurface in $\mathbb R^4$ of low entropy does not disconnect

Jacob Bernstein; Shengwen Wang

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arXiv · 1801.05083

The level set flow of a hypersurface in $\mathbb R^4$ of low entropy does not disconnect

Jacob Bernstein·Shengwen Wang

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Abstract

We show that if $\Sigma\subset \mathbb R^4$ is a closed, connected hypersurface with entropy $\lambda(\Sigma)\leq \lambda(\mathbb{S}^2\times \mathbb R)$, then the level set flow of $\Sigma$ never disconnects. We also obtain a sharp version of the forward clearing out lemma for non-fattening flows in $\mathbb R^4$ of low entropy.

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BibTeX RIS

Jacob Bernstein, Shengwen Wang. 2018-01-16. The level set flow of a hypersurface in $\mathbb R^4$ of low entropy does not disconnect. https://arxiv.org/abs/1801.05083

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