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Isospectrality for Orbifold Lens Spaces

Part of: Partial differential equations on manifolds; differential operators Global differential geometry

Published online by Cambridge University Press:  27 August 2019

Naveed S. Bari  and
Eugenie Hunsicker
Naveed S. Bari
Affiliation:
47 Lloyd Wright Avenue, Manchester M11 3NJ, United Kingdom Email: bari.naveed@yahoo.com
Eugenie Hunsicker
Affiliation:
Department of Mathematics, Loughborough University, Loughborough, LE11 3TU, United Kingdom Email: E.Hunsicker@lboro.ac.uk
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Abstract

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.

Keywords

spectral geometryglobal Riemannian geometryorbifoldlens space

MSC classification

Primary: 58J53: Isospectrality
Secondary: 53C20: Global Riemannian geometry, including pinching
Type
Article
Information
Canadian Journal of Mathematics , Volume 72 , Issue 2 , April 2020 , pp. 281 - 325
Copyright
© Canadian Mathematical Society 2019

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