We answer Mark Kac’s famous question [K], “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.
Published inCanadian Journal of Mathematics
CitationBARI, N.S. and HUNSICKER, E., 2019. Isospectrality for orbifold lens spaces. Canadian Journal of Mathematics, 72(2), pp. 281-325.
PublisherCambridge University Press © Canadian Mathematical Society
VersionAM (Accepted Manuscript)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
NotesThis article has been published in a revised form in Canadian Journal of Mathematics https://doi.org/10.4153/s0008414x19000178. This version is published under a Creative Commons CC-BY-NC-ND. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed. © Canadian Mathematical Society.