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Sbornik: Mathematics, 2013, Volume 204, Issue 12, Pages 1728–1744
DOI: https://doi.org/10.1070/SM2013v204n12ABEH004358 (Mi sm8227) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Nonmaximality of known extremal metrics on torus and Klein bottle

M. A. Karpukhinab

a M. V. Lomonosov Moscow State University
b Independent University of Moscow
English version PDF (499 kB) Citations (10)
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DOI: https://doi.org/10.1070/SM2013v204n12ABEH004358
Abstract: 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.
Keywords: extremal metrics, bipolar surface, Otsuki tori, Lawson tau-surfaces.
Funding agency Grant number
Dobrushin Foundation
Simons Foundation
Received: 27.02.2013 and 10.06.2013
Russian version:
Matematicheskii Sbornik, 2013, Volume 204, Number 12, Pages 31–48
DOI: https://doi.org/10.4213/sm8227
Bibliographic databases:
Document Type: Article
UDC: 514.764.21
MSC: 58E11
Language: English
Original paper language: Russian
Citation: M. A. Karpukhin, “Nonmaximality of known extremal metrics on torus and Klein bottle”, Mat. Sb., 204:12 (2013), 31–48; Sb. Math., 204:12 (2013), 1728–1744
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:37
    First page:23
     
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