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 ) $\lambda_{1} (M)$...

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Main Author:	Keomkyo Seo
Format:	Article
Language:	English
Published:	SpringerOpen 2016-04-01
Series:	Journal of Inequalities and Applications
Subjects:	minimal hypersurface finite index hyperbolic space fundamental tone eigenvalue
Online Access:	http://link.springer.com/article/10.1186/s13660-016-1071-7

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spelling	doaj-1cb43f3fa116475e9a4a3ceb2f984c002020-11-24T21:59:19ZengSpringerOpenJournal 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
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Keomkyo Seo
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
author_facet	Keomkyo Seo
author_sort	Keomkyo Seo
title	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_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_sort	fundamental tone of minimal hypersurfaces with finite index in hyperbolic space
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2016-04-01
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 $n^{2}$ .
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
_version_	1725847806894145536

Fundamental tone of minimal hypersurfaces with finite index in hyperbolic space

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