A second eigenvalue bound for the Dirichlet Laplacian in hyperbolic space
- 1 November 2007
- journal article
- Published by Duke University Press in Duke Mathematical Journal
- Vol. 140 (2) , 245-279
Abstract
Let Ω be some domain in the hyperbolic space Hn (with n≥2), and let S1 be a geodesic ball that has the same first Dirichlet eigenvalue as Ω. We prove the Payne-Pólya-Weinberger (PPW) conjecture for Hn, namely, that the second Dirichlet eigenvalue on Ω is smaller than or equal to the second Dirichlet eigenvalue on S1. We also prove that the ratio of the first two eigenvalues on geodesic balls is a decreasing function of the radiusKeywords
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