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

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
18
Publisher
Duke University Press
Pages
8752-8798
Publication identifier
http://dx.doi.org/10.1093/imrn/rnu211
Metadata
Show full item record
Author(s)
Lamboley, Jimmy
Sicbaldi, Pieralberto
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

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