A classical theorem of A. D. Alexandrov says that a connected compact smooth hypersurface in Euclidean space with constant mean curvature must be a sphere. We give exposition to some results on symmetry properties of hypersurfaces with ordered mean curvature and associated variations of the Hopf Lemma. Some open problems will be discussed.
Citation: YanYan Li. Symmetry of hypersurfaces and the Hopf Lemma[J]. Mathematics in Engineering, 2023, 5(5): 1-9. doi: 10.3934/mine.2023084
A classical theorem of A. D. Alexandrov says that a connected compact smooth hypersurface in Euclidean space with constant mean curvature must be a sphere. We give exposition to some results on symmetry properties of hypersurfaces with ordered mean curvature and associated variations of the Hopf Lemma. Some open problems will be discussed.
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YanYan Li. Symmetry of hypersurfaces and the Hopf Lemma[J]. Mathematics in Engineering, 2023, 5(5): 1-9. doi: 10.3934/mine.2023084
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