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

Erwann Delay | Zendy; Pieralberto Sicbaldi | Zendy

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

Author(s) -

Erwann Delay,

Pieralberto Sicbaldi

Publication year - 2015

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2015.35.5799

Subject(s) - riemannian manifold , scalar curvature , mathematics , laplace–beltrami operator , ricci curvature , eigenvalues and eigenvectors , pure mathematics , manifold (fluid mechanics) , mathematical analysis , pseudo riemannian manifold , hermitian manifold , exponential map (riemannian geometry) , curvature , prescribed scalar curvature problem , sectional curvature , physics , geometry , p laplacian , quantum mechanics , mechanical engineering , engineering , boundary value problem

International audienceWe 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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