## J. Bernstein - S. Wang

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

created by wang on 13 Nov 2020

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BibTeX]

*Accepted Paper*

**Inserted:** 13 nov 2020

**Last Updated:** 13 nov 2020

**Journal:** Communications in Analysis and Geometry

**Year:** 2018

**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.