Symmetry of hypersurfaces and the Hopf Lemma
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 Lem...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-10-01
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| Series: | Mathematics in Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2023084?viewType=HTML |
| _version_ | 1827631113861857280 |
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| author | YanYan Li |
| author_facet | YanYan Li |
| author_sort | YanYan Li |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T14:16:29Z |
| format | Article |
| id | doaj.art-2fe5a1b157b745a79e90b144b88a106d |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-03-09T14:16:29Z |
| publishDate | 2023-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-2fe5a1b157b745a79e90b144b88a106d2023-11-29T01:11:19ZengAIMS PressMathematics in Engineering2640-35012023-10-01551910.3934/mine.2023084Symmetry of hypersurfaces and the Hopf LemmaYanYan Li 0Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854, USAA 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.https://www.aimspress.com/article/doi/10.3934/mine.2023084?viewType=HTMLsymmetryhypersurfacesmean curvaturehigher order curvaturehopf lemma |
| spellingShingle | YanYan Li Symmetry of hypersurfaces and the Hopf Lemma Mathematics in Engineering symmetry hypersurfaces mean curvature higher order curvature hopf lemma |
| title | Symmetry of hypersurfaces and the Hopf Lemma |
| title_full | Symmetry of hypersurfaces and the Hopf Lemma |
| title_fullStr | Symmetry of hypersurfaces and the Hopf Lemma |
| title_full_unstemmed | Symmetry of hypersurfaces and the Hopf Lemma |
| title_short | Symmetry of hypersurfaces and the Hopf Lemma |
| title_sort | symmetry of hypersurfaces and the hopf lemma |
| topic | symmetry hypersurfaces mean curvature higher order curvature hopf lemma |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2023084?viewType=HTML |
| work_keys_str_mv | AT yanyanli symmetryofhypersurfacesandthehopflemma |