Annals of Global Analysis and Geometry

, Volume 44, Issue 4, pp 501–515 | Cite as

Isospectral Alexandrov spaces



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.


Alexandrov space Spectral geometry Laplace operator Isospectrality 

Mathematics Subject Classification (2000)

58J53 58J50 53C20 51F99 



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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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institut für MathematikUniversität AugsburgAugsburgGermany
  2. 2.Departamento de MatemáticaUniversidade Federal de Santa CatarinaFlorianópolis-SCBrazil

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