Domain deformations and eigenvalues of the Dirichlet Laplacian in a Riemannian manifold
| dc.creator | Soufi, Ahmad El | |
| dc.creator | Ilias, Saïd | |
| dc.date | 2007-05-09 | |
| dc.date.accessioned | 2026-07-07T08:31:37Z | |
| dc.date.available | 2026-07-07T08:31:37Z | |
| dc.description | For any bounded regular domain $Ω$ of a real analytic Riemannian manifold $M$, we denote by $λ_{k}(Ω)$ the $k$-th eigenvalue of the Dirichlet Laplacian of $Ω$. In this paper, we consider $λ_k$ and as a functional upon the set of domains of fixed volume in $M$. We introduce and investigate a natural notion of critical domain for this functional. In particular, we obtain necessary and sufficient conditions for a domain to be critical, locally minimizing or locally maximizing for $λ_k$. These results rely on Hadamard type variational formulae that we establish in this general setting. | |
| dc.description | To appear in Illinois J. Math | |
| dc.identifier | https://arxiv.org/abs/0705.1263 | |
| dc.identifier | http://arxiv.org/abs/0705.1263 | |
| dc.identifier | Illinois Journal of Mathematics 51 (2007) 645--666 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138550 | |
| dc.subject | Metric Geometry | |
| dc.subject | Spectral Theory | |
| dc.subject | 49R50, 35P99, 58J50, 58J32 | |
| dc.title | Domain deformations and eigenvalues of the Dirichlet Laplacian in a Riemannian manifold | |
| dc.type | text |