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Extremal domains for the first eigenvalue in a general compact Riemannian manifold

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  • 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.
    Mathematics Subject Classification: Primary: 49Q10, 53B20, 53C21; Secondary: 53A10, 35N25, 58C40.

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