Isospectral metrics on weighted projective spaces

Abstract

We construct the first examples of families of bad Riemannian orbifolds which are isospectral with respect to the Laplacian but not isometric. In our case these are particular fixed weighted projective spaces equipped with isospectral metrics obtained by a generalization of Schüth's version of the torus method.

29 pages, no figures; v3 with more detailed proofs in Section 3.1 and one corrected proof in Section 3.2