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

Jimmy Lamboley; Pieralberto Sicbaldi

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arXiv · 1406.5167

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

Jimmy Lamboley·Pieralberto Sicbaldi

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Abstract

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

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BibTeX RIS

Jimmy Lamboley, Pieralberto Sicbaldi. 2014-06-20. New examples of extremal domains for the first eigenvalue of the Laplace-Beltrami operator in a Riemannian manifold with boundary. https://arxiv.org/abs/1406.5167

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