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Genre/Form: article in peer-reviewed journal Material Type: Internet resource Document Type: Internet Resource, Archival Material All Authors / Contributors: Grosjean, Jean-Francois; Roth, Julien OCLC Number: 784460955 Language Note: English Abstract: In this paper we give pinching theorems for the first nonzero eigenvalue of the Laplacian on the compact hypersurfaces of ambient spaces with bounded sectional curvature. As application we deduce rigidity results for stable constant mean curvature hypersurfaces $M$ of these spaces $N$. Indeed, we prove that if $M$ is included in a ball of radius small enough then the Hausdorff-distance between $M$ and a geodesic sphere $S$ of $N$ is small. Moreover $M$ is diffeomorphic and quasi-isometric to $S$. As other application, we give rigidity results for almost umbilic hypersurfaces.

Title : Eigenvalue pinching and application to the stability and the almost umbilicity of hypersurfaces
Author : Grosjean, Jean-Francois; Roth, Julien
Language : en
Rating :
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Type : PDF, ePub, Kindle
Uploaded : Apr 12, 2021

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