Pincement spectral en courbure de Ricci positive

2005/04/08 by Jérôme Bertrand, Jerome Bertrand, Bertrand, Jerome · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #math.SP

paper · pdf · doi:10.48550/arxiv.math/0504173

arxiv created 2005/04/08 · arxiv updated 2009/12/01

Abstract

We show that for n dimensional manifolds whose the Ricci curvature is greater or equal to n-1 and for k in 1,...,n+1, the k-th eigenvalue for the Laplacian is close to n if and only if the manifold contains a subset which is Gromov-Hausdorff close to the unit sphere of dimension k-1. For k=n+1, this gives a new proof of results of Colding and Petersen which show that the (n+1)-th eigenvalue is close to n if and only if the manifold is Gromov-Hausdorff close to the n-sphere.

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