Critical metrics of the eigenvalue gaps of Laplace‐Beltrami operators | Zendy

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Critical metrics of the eigenvalue gaps of Laplace‐Beltrami operators

Author(s) -

Hou Songbo

Publication year - 2011

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200710199

Subject(s) - mathematics , laplace operator , conformal map , eigenvalues and eigenvectors , metric (unit) , manifold (fluid mechanics) , class (philosophy) , space (punctuation) , dimension (graph theory) , pure mathematics , riemannian manifold , mathematical analysis , computer science , physics , mechanical engineering , operations management , quantum mechanics , operating system , artificial intelligence , engineering , economics

Let M be a compact smooth manifold of dimension n ⩾ 2. We investigate critical metrics of the Laplacian eigenvalue gaps considered as functionals on the space of Riemannian metrics or a conformal class of metrics on M . We give necessary and sufficient conditions for a metric to be critical for such a functional. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim

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