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On the Multiplicity of Eigenvalues of the Laplacian on Surfaces

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Abstract

We show that the multiplicity of the eigenvalues of the Laplace Beltrami operator on compact Riemannian surfaces with genus zero is bounded by m(λk) ≤ 2k − 3 for k ≥ 3. Here we label the eigenvalues in the following way: 0 = λ1 < λ2 ≤ λ3 . . ..

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Authors and Affiliations

  1. Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090, Wien, Austria (E-mail

    M. Hoffmann-Ostenhof

  2. Institut für Theoretische Chemie, Universität Wien, Währinger Strasse 17, A-1090, Wien, Austria

    T. Hoffmann-Ostenhof

  3. International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, A-1090, Wien, Austria (E-mail

    T. Hoffmann-Ostenhof

  4. International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, A-1090 Wien, Austria and Institute for Problems of Information Transmission, Bol'shoi Karetnyi 19, 101447, Moscow, Russia

    N. Nadirashvili

Authors
  1. M. Hoffmann-Ostenhof
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  2. T. Hoffmann-Ostenhof
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  3. N. Nadirashvili
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Hoffmann-Ostenhof, M., Hoffmann-Ostenhof, T. & Nadirashvili, N. On the Multiplicity of Eigenvalues of the Laplacian on Surfaces. Annals of Global Analysis and Geometry 17, 43–48 (1999). https://doi.org/10.1023/A:1006595115793

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