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Extremal domains for the first eigenvalue of the Laplace-Beltrami operator

Frank Pacard; Pieralberto Sicbaldi — 2009

Annales de l’institut Fourier

We prove the existence of extremal domains with small prescribed volume for the first eigenvalue of Laplace-Beltrami operator in some Riemannian manifold. These domains are close to geodesic spheres of small radius centered at a nondegenerate critical point of the scalar curvature.

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