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Isospectral Alexandrov spaces

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Abstract

We construct the first non-trivial examples of compact non-isometric Alexandrov spaces which are isospectral with respect to the Laplacian and not isometric to Riemannian orbifolds. This construction generalizes independent earlier results by the authors based on Schüth’s version of the torus method.

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Acknowledgments

The first author’s work was partly funded by the Studienstiftung des Deutschen Volkes, the graduate program TopMath of the Elite Network of Bavaria and the TopMath Graduate Center of TUM Graduate School at Technische Universität München. He is grateful to Bernhard Hanke for the guidance and support during the work on his Bachelor’s thesis and his Master’s degree. The second author was partly funded by FAPESP and Funpesquisa-UFSC. Both authors would like to thank Marcos Alexandrino, Dorothee Schüth and the referee for various helpful suggestions.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Augsburg, 86135 , Augsburg, Germany

    Alexander Engel

  2. Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900 , Florianópolis-SC, Brazil

    Martin Weilandt

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  1. Alexander Engel
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  2. Martin Weilandt
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Correspondence to Martin Weilandt.

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Engel, A., Weilandt, M. Isospectral Alexandrov spaces. Ann Glob Anal Geom 44, 501–515 (2013). https://doi.org/10.1007/s10455-013-9378-9

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  • DOI: https://doi.org/10.1007/s10455-013-9378-9

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