Fundamental tone of minimal hypersurfaces with finite index in hyperbolic space
Abstract Let M be a complete minimal hypersurface in hyperbolic space H n + 1 ( − 1 ) $\mathbb {H}^{n+1}(-1)$ with constant sectional curvature −1. We prove that if M has a finite index and finite L 2 $L^{2}$ norm of the second fundamental form, then the fundamental tone λ 1 ( M ) $\lambda_{1} (M)$...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2016-04-01
|
| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1071-7 |
| _version_ | 1819136009437184000 |
|---|---|
| author | Keomkyo Seo |
| author_facet | Keomkyo Seo |
| author_sort | Keomkyo Seo |
| collection | DOAJ |
| description | Abstract Let M be a complete minimal hypersurface in hyperbolic space H n + 1 ( − 1 ) $\mathbb {H}^{n+1}(-1)$ with constant sectional curvature −1. We prove that if M has a finite index and finite L 2 $L^{2}$ norm of the second fundamental form, then the fundamental tone λ 1 ( M ) $\lambda_{1} (M)$ is bounded above by n 2 $n^{2}$ . |
| first_indexed | 2024-12-22T10:28:10Z |
| format | Article |
| id | doaj.art-1cb43f3fa116475e9a4a3ceb2f984c00 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-22T10:28:10Z |
| publishDate | 2016-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-1cb43f3fa116475e9a4a3ceb2f984c002022-12-21T18:29:24ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-04-01201611510.1186/s13660-016-1071-7Fundamental tone of minimal hypersurfaces with finite index in hyperbolic spaceKeomkyo Seo0Department of Mathematics, Sookmyung Women’s UniversityAbstract Let M be a complete minimal hypersurface in hyperbolic space H n + 1 ( − 1 ) $\mathbb {H}^{n+1}(-1)$ with constant sectional curvature −1. We prove that if M has a finite index and finite L 2 $L^{2}$ norm of the second fundamental form, then the fundamental tone λ 1 ( M ) $\lambda_{1} (M)$ is bounded above by n 2 $n^{2}$ .http://link.springer.com/article/10.1186/s13660-016-1071-7minimal hypersurfacefinite indexhyperbolic spacefundamental toneeigenvalue |
| spellingShingle | Keomkyo Seo Fundamental tone of minimal hypersurfaces with finite index in hyperbolic space Journal of Inequalities and Applications minimal hypersurface finite index hyperbolic space fundamental tone eigenvalue |
| title | Fundamental tone of minimal hypersurfaces with finite index in hyperbolic space |
| title_full | Fundamental tone of minimal hypersurfaces with finite index in hyperbolic space |
| title_fullStr | Fundamental tone of minimal hypersurfaces with finite index in hyperbolic space |
| title_full_unstemmed | Fundamental tone of minimal hypersurfaces with finite index in hyperbolic space |
| title_short | Fundamental tone of minimal hypersurfaces with finite index in hyperbolic space |
| title_sort | fundamental tone of minimal hypersurfaces with finite index in hyperbolic space |
| topic | minimal hypersurface finite index hyperbolic space fundamental tone eigenvalue |
| url | http://link.springer.com/article/10.1186/s13660-016-1071-7 |
| work_keys_str_mv | AT keomkyoseo fundamentaltoneofminimalhypersurfaceswithfiniteindexinhyperbolicspace |