Volume 22, issue 2 (2018)

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Topology of closed hypersurfaces of small entropy

Jacob Bernstein and Lu Wang

Geometry & Topology 22 (2018) 1109–1141
Abstract

We use a weak mean curvature flow together with a surgery procedure to show that all closed hypersurfaces in ${ℝ}^{4}$ with entropy less than or equal to that of ${\mathbb{S}}^{2}×ℝ$, the round cylinder in ${ℝ}^{4}$, are diffeomorphic to ${\mathbb{S}}^{3}$.

Keywords
mean curvature flow, surgery, entropy, self-shrinker
Mathematical Subject Classification 2010
Primary: 53C44
Secondary: 35K55, 57R65