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Inverse boundary spectral problem for Riemannian polyhedra

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Abstract

We consider a Riemannian polyhedron of a special type with a piecewise smooth boundary. The associated Neumann Laplacian defines the boundary spectral data as the set of eigenvalues and restrictions to the boundary of the corresponding eigenfunctions. In this paper we prove that the boundary spectral data prescribed on an open subset of the polyhedron boundary determine this polyhedron uniquely, i.e. up to an isometry.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Glasgow, 15 University Garden, Glasgow, G12 8QW, UK

    Anna Kirpichnikova

  2. Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK

    Yaroslav Kurylev

Authors
  1. Anna Kirpichnikova
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  2. Yaroslav Kurylev
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Correspondence to Yaroslav Kurylev.

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Kirpichnikova, A., Kurylev, Y. Inverse boundary spectral problem for Riemannian polyhedra. Math. Ann. 354, 1003–1028 (2012). https://doi.org/10.1007/s00208-011-0758-9

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  • DOI: https://doi.org/10.1007/s00208-011-0758-9

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