A Variational Problem and Classification Theorem for Extremal Hypersurfaces in the Space Form
The classification of the isoparametric extremal hypersurfaces in the space form is obtained in this paper. We also derived the Euler-Lagrange equation for extremal hypersurface and obtained Simons’ type integral inequality. When the integral equality holds, we can obtain the characteristics of isop...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/5881125 |
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| _version_ | 1849472806689964032 |
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| author | Yu-Chung Chang |
| author_facet | Yu-Chung Chang |
| author_sort | Yu-Chung Chang |
| collection | DOAJ |
| description | The classification of the isoparametric extremal hypersurfaces in the space form is obtained in this paper. We also derived the Euler-Lagrange equation for extremal hypersurface and obtained Simons’ type integral inequality. When the integral equality holds, we can obtain the characteristics of isoparametric extremal hypersurfaces by using this classification theorem. The classification of isoparametric extremal hypersurfaces in the space form is the first study that has not been seen in the previous literature. |
| format | Article |
| id | doaj-art-dae0daaef6d14f5e9f101ea326557a72 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-dae0daaef6d14f5e9f101ea326557a722025-08-20T03:24:25ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/5881125A Variational Problem and Classification Theorem for Extremal Hypersurfaces in the Space FormYu-Chung Chang0School of ManagementThe classification of the isoparametric extremal hypersurfaces in the space form is obtained in this paper. We also derived the Euler-Lagrange equation for extremal hypersurface and obtained Simons’ type integral inequality. When the integral equality holds, we can obtain the characteristics of isoparametric extremal hypersurfaces by using this classification theorem. The classification of isoparametric extremal hypersurfaces in the space form is the first study that has not been seen in the previous literature.http://dx.doi.org/10.1155/2022/5881125 |
| spellingShingle | Yu-Chung Chang A Variational Problem and Classification Theorem for Extremal Hypersurfaces in the Space Form Journal of Mathematics |
| title | A Variational Problem and Classification Theorem for Extremal Hypersurfaces in the Space Form |
| title_full | A Variational Problem and Classification Theorem for Extremal Hypersurfaces in the Space Form |
| title_fullStr | A Variational Problem and Classification Theorem for Extremal Hypersurfaces in the Space Form |
| title_full_unstemmed | A Variational Problem and Classification Theorem for Extremal Hypersurfaces in the Space Form |
| title_short | A Variational Problem and Classification Theorem for Extremal Hypersurfaces in the Space Form |
| title_sort | variational problem and classification theorem for extremal hypersurfaces in the space form |
| url | http://dx.doi.org/10.1155/2022/5881125 |
| work_keys_str_mv | AT yuchungchang avariationalproblemandclassificationtheoremforextremalhypersurfacesinthespaceform AT yuchungchang variationalproblemandclassificationtheoremforextremalhypersurfacesinthespaceform |