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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
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