Isospectrality for Orbifold Lens Spaces

We answer Mark Kac’s famous question, “Can one hear the shape of a drum?” in the positive for orbifolds that are 3-dimensional and 4-dimensional lens spaces; we thus complete the answer to this question for orbifold lens spaces in all dimensions. We also show that the coefficients of the asymptotic...

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Bibliographic Details
Published in:Canadian journal of mathematics 2020-04, Vol.72 (2), p.281-325
Main Authors: Bari, Naveed S., Hunsicker, Eugenie
Format: Article
Language:English
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Summary:We answer Mark Kac’s famous question, “Can one hear the shape of a drum?” in the positive for orbifolds that are 3-dimensional and 4-dimensional lens spaces; we thus complete the answer to this question for orbifold lens spaces in all dimensions. We also show that the coefficients of the asymptotic expansion of the trace of the heat kernel are not sufficient to determine the above results.
ISSN:0008-414X
1496-4279
DOI:10.4153/S0008414X19000178