Naveed Shamsul Bari

  1. Orbifold Lens Spaces that are Isospectral but not Isometric.

    Authors: Naveed Shamsul Bari
    Subjects: Spectral Theory
    Abstract

    We answer Mark Kacs famous question - can one hear the shape of a drum - in
    the negative for orbifolds that are spherical space forms. This is done by
    extending the techniques developed by A. Ikeda on Lens Spaces to the orbifold
    setting. Several results are proved to show that with certain restrictions on
    the dimensionalities of orbifold Lens spaces we can obtain infinitely many
    pairs of isospectral non-isometric Lens spaces. These results are then
    generalized to show that for any dimension greater than 8 we can have pairs of
    isospectral non-isometric orbifold Lens spaces.

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