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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Main Author: Yu-Chung Chang
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2022/5881125
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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.
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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
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AT yuchungchang variationalproblemandclassificationtheoremforextremalhypersurfacesinthespaceform