Topology of closed hypersurfaces of small entropy

Bernstein, Jacob¹ ; Wang, Lu²

¹ Department Of Mathematics, Johns Hopkins University, Baltimore, MD, United States
² Department of Mathematics, University of Wisconsin, Madison, WI, United States

Geometry & topology, Tome 22 (2018) no. 2, pp. 1109-1141.

Résumé

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 ${\mathbb{S}}^2\times ℝ$, the round cylinder in ${ℝ}^4$, are diffeomorphic to ${\mathbb{S}}^3$.

Détail

DOI : 10.2140/gt.2018.22.1109

Classification : 53C44, 35K55, 57R65
Keywords: mean curvature flow, surgery, entropy, self-shrinker

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