Isospectral orbifolds with different maximal isotropy orders |
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Authors: | Juan Pablo Rossetti Dorothee Schueth Martin Weilandt |
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Institution: | 1.Famaf-CIEM,Universidad Nacional de Córdoba,Córdoba,Argentina;2.Institut für Mathematik,Humboldt-Universit?t zu Berlin,Berlin,Germany |
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Abstract: | 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 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.
All three authors were partially supported by DFG Sonderforschungsbereich 647. |
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Keywords: | Laplace operator Isospectral orbifolds Isotropy orders |
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