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Title: Nonmaximality of known extremal metrics on torus and Klein bottle

The El Soufi-Ilias theorem establishes a connection between minimal submanifolds of spheres and extremal metrics for eigenvalues of the Laplace-Beltrami operator. Recently, this connection was used to provide several explicit examples of extremal metrics. We investigate the properties of these metrics and prove that none of them is maximal. Bibliography: 24 titles.
Authors:
 [1]
  1. M. V. Lomonosov Moscow State University, Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
22365850
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 204; Journal Issue: 12; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; EIGENVALUES; MATHEMATICAL MANIFOLDS; MATHEMATICAL OPERATORS; MATHEMATICAL SOLUTIONS; METRICS