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Topology of closed hypersurfaces of small entropy. (English) Zbl 1381.53112
Summary: We use a weak mean curvature flow together with a surgery procedure to show that all closed hypersurfaces in $$\mathbb R^4$$ with entropy less than or equal to that of $$\mathbb{S}^2\times \mathbb R$$, the round cylinder in $$\mathbb R^4$$, are diffeomorphic to $$\mathbb{S}^3$$.

##### MSC:
 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) 35K55 Nonlinear parabolic equations 57R65 Surgery and handlebodies
##### Keywords:
mean curvature flow; surgery; entropy; self-shrinker
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