Extremal metrics for eigenvalues of the Laplace-Beltrami operator on surfaces

DOI10.1070/RM2013v068n06ABEH004870zbMath1328.53078OpenAlexW2025517278MaRDI QIDQ5410961

Alexei V. Penskoi

Publication date: 17 April 2014

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/rm2013v068n06abeh004870

zbMATH Keywords

extremal metricgeometric optimization of eigenvalues

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Differential forms in global analysis (58A10) Optimization of shapes other than minimal surfaces (49Q10) Critical metrics (58E11) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02)

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