Calculus of Variations and Geometric Measure Theory

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


Accepted Paper

Inserted: 13 nov 2020
Last Updated: 13 nov 2020

Journal: Communications in Analysis and Geometry
Year: 2018

ArXiv: 1801.05083 PDF


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.