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On the compactness of hypersurfaces with finite total curvature via mean curvature flow
Journal of Geometry and Physics ( IF 1.6 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.geomphys.2020.103857
Shunjuan Cao , Entao Zhao

Abstract Given a complete hypersurface in the Euclidean space, we assume that the second fundamental form is bounded and the mean curvature is bounded from below by a positive constant. We prove that if the L p -norm of the trace-free second fundamental form for some p ≥ 2 is finite, then the hypersurface is compact.

中文翻译:

基于平均曲率流的有限总曲率超曲面的紧致性

摘要 给定欧几里得空间中的完整超曲面,我们假设第二基本形式是有界的,平均曲率从下方以正常数为界。我们证明,如果某些 p ≥ 2 的无迹第二基本形式的 L p 范数是有限的,则超曲面是紧致的。
更新日期:2020-12-01
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