Original Paper

Annals of Global Analysis and Geometry

, Volume 34, Issue 4, pp 351-366

First online:

Isospectral orbifolds with different maximal isotropy orders

  • Juan Pablo RossettiAffiliated withFamaf-CIEM, Universidad Nacional de Córdoba
  • , Dorothee SchuethAffiliated withInstitut für Mathematik, Humboldt-Universität zu Berlin Email author 
  • , Martin WeilandtAffiliated withInstitut für Mathematik, Humboldt-Universität zu Berlin

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We construct pairs of compact Riemannian orbifolds which are isospectral for the Laplace operator on functions such that the maximal isotropy order of singular points in one of the orbifolds is higher than in the other. In one type of examples, isospectrality arises from a version of the famous Sunada theorem which also implies isospectrality on p-forms; here the orbifolds are quotients of certain compact normal homogeneous spaces. In another type of examples, the orbifolds are quotients of Euclidean \({\mathbb{R}^3}\) and are shown to be isospectral on functions using dimension formulas for the eigenspaces developed in [12]. In the latter type of examples the orbifolds are not isospectral on 1-forms. Along the way we also give several additional examples of isospectral orbifolds which do not have maximal isotropy groups of different size but other interesting properties.


Laplace operator Isospectral orbifolds Isotropy orders

Mathematics Subject Classification (2000)

58J53 58J50 53C20