05-387 Rafael D. Benguria, Helmut Linde
A second eigenvalue bound for the Dirichlet Laplacian in hyperbolic space (320K, Postscript) Nov 11, 05
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. Let $\Omega$ be some domain in the hyperbolic space $\Hn$ (with $n\ge 2$) and $S_1$ the geodesic ball that has the same first Dirichlet eigenvalue as $\Omega$. We prove the Payne-P\'olya-Weinberger conjecture for $\Hn$, i.e., that the second Dirichlet eigenvalue on $\Omega$ is smaller or equal than the second Dirichlet eigenvalue on $S_1$. We also prove that the ratio of the first two eigenvalues on geodesic balls is a decreasing function of the radius.

Files: 05-387.src( 05-387.keywords , PPW for H_n.ps )