Extremal domains for the first eigenvalue of the Laplace-Beltrami operator
Annales de l'Institut Fourier, Volume 59 (2009) no. 2, pp. 515-542.

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.

Nous prouvons l’existence de domaines extrémaux avec volume petit et fixé pour la première valeur propre de l’opérateur de Laplace-Beltrami dans certaines variétés riemanniennes. Ces domaines ressemblent à des sphères géodésiques de rayon petit centrées en un point critique non dégénéré de la courbure scalaire.

Received:
Accepted:
DOI: 10.5802/aif.2438
Classification: 53B20
Keywords: Extremal domain, Laplace-Beltrami operator, first eigenvalue, scalar curvature, geodesic sphere
Pacard, Frank 1; Sicbaldi, Pieralberto 2

1 Université Paris Est UFR des Sciences et Technologie Bâtiment P3 - 4e étage 61, avenue du Général de Gaulle 94010 Créteil Cedex (France)
2 Université Paris 12 UFR des Sciences et Technologie Bâtiment P3 - 4e étage 61, avenue du Général de Gaulle 94010 Créteil Cedex (France)
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Pacard, Frank; Sicbaldi, Pieralberto. Extremal domains for the first eigenvalue of the Laplace-Beltrami operator. Annales de l'Institut Fourier, Volume 59 (2009) no. 2, pp. 515-542. doi : 10.5802/aif.2438. https://aif.centre-mersenne.org/articles/10.5802/aif.2438/

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