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On the second eigenvalue of the dirichlet laplacian

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Abstract

The multiplicity of the second eigenvalue of the Dirichlet Laplacian on smooth Riemannian surfaces with boundary that satisfy certain convexity condition is at most two. The proof is based on variational formulas for eigenvalues under the change of the domain.

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Author notes

  1. L. Friedlander

    Present address: Department of Mathematics, University of Arizona, 85721, Tucson, AZ, U.S.A.

Authors and Affiliations

  1. Department of Mathematics, University of California, 90024-1555, Los Angeles, CA

    L. Friedlander

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  1. L. Friedlander
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Friedlander, L. On the second eigenvalue of the dirichlet laplacian. Israel J. Math. 79, 23–32 (1992). https://doi.org/10.1007/BF02764800

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  • DOI: https://doi.org/10.1007/BF02764800

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