Isospectral spherical space forms and orbifolds of highest volume

Abstract

We prove that vol(S d)/8 is the highest volume of a pair of ddimensional isospectral and non-isometric spherical orbifolds for any d ≥ 5. Furthermore, we show that vol(S 2n−1 )/11 is the highest volume of a pair of (2n − 1)-dimensional isospectral and non-isometric spherical space forms if either n ≥ 11 and n ≡ 1 (mod 5), or n ≥ 7 and n ≡ 2 (mod 5), or n ≥ 3 and n ≡ 3 (mod 5).