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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