New examples of extremal domains for the first eigenvalue of the Laplace-Beltrami operator in a Riemannian manifold with boundary

Lamboley, Jimmy; Sicbaldi, Pieralberto

Lamboley, Jimmy; Sicbaldi, Pieralberto (2015), New examples of extremal domains for the first eigenvalue of the Laplace-Beltrami operator in a Riemannian manifold with boundary, International Mathematics Research Notices, 2015, 18, p. 8752-8798. http://dx.doi.org/10.1093/imrn/rnu211

Type

Article accepté pour publication ou publié

External document link

https://arxiv.org/abs/1406.5167v2

Date

2015

Journal name

International Mathematics Research Notices

Volume

2015

Number

Publisher

Duke University Press

Pages

8752-8798

Abstract (EN)

We build new examples of extremal domains with small prescribed volume for the first eigenvalue ofthe Laplace-Beltrami operator in some Riemannian manifold with boundary. These domains are close to half ballsof small radius centered at a nondegenerate critical point of the mean curvature function of the boundary of themanifold, and their boundary intersects the boundary of the manifold orthogonally.

Subjects / Keywords

Laplace-Beltrami operator; Riemannian manifold