Extremal domains for the first eigenvalue in a general Riemannian manifold

Erwann Delay; Pieralberto Sicbaldi

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arXiv · 1302.4221

Extremal domains for the first eigenvalue in a general Riemannian manifold

Erwann Delay·Pieralberto Sicbaldi

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Abstract

We prove the existence of extremal domains with small prescribed volume for the first eigenvalue of the Laplace-Beltrami operator in any compact Riemannian manifold. This result generalizes a results of F. Pacard and the second author where the existence of a nondegenerate critical point of the scalar curvature of the Riemannian manifold was required.

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BibTeX RIS

Erwann Delay, Pieralberto Sicbaldi. 2013-02-18. Extremal domains for the first eigenvalue in a general Riemannian manifold. https://arxiv.org/abs/1302.4221

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