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

DOI : https://doi.org/10.5802/aif.2438
Classification:  53B20
Keywords: Extremal domain, Laplace-Beltrami operator, first eigenvalue, scalar curvature, geodesic sphere
@article{AIF_2009__59_2_515_0,
     author = {Pacard, Frank and Sicbaldi, Pieralberto},
     title = {Extremal domains for the first eigenvalue of the Laplace-Beltrami operator},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {59},
     number = {2},
     year = {2009},
     pages = {515-542},
     doi = {10.5802/aif.2438},
     mrnumber = {2521426},
     zbl = {1166.53029},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2009__59_2_515_0}
}
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. http://www.numdam.org/item/AIF_2009__59_2_515_0/

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