A second eigenvalue bound for the Dirichlet Laplacian in hyperbolic space
| dc.creator | Benguria, Rafael D. | |
| dc.creator | Linde, Helmut | |
| dc.date | 2005-11-11 | |
| dc.date.accessioned | 2026-07-07T06:50:30Z | |
| dc.date.available | 2026-07-07T06:50:30Z | |
| dc.description | Let $Ω$ 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 $Ω$. We prove the Payne-Pólya-Weinberger conjecture for $\Hn$, i.e., that the second Dirichlet eigenvalue on $Ω$ 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. | |
| dc.identifier | https://arxiv.org/abs/math-ph/0511045 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0511045 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104685 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35P15; 49Rxx; 58Jxx | |
| dc.title | A second eigenvalue bound for the Dirichlet Laplacian in hyperbolic space | |
| dc.type | text |