Revista de la
Unión Matemática Argentina
Isospectral spherical space forms and orbifolds of highest volume
Alfredo Álzaga and Emilio A. Lauret

Volume 69, no. 1 (2026), pp. 71–91    

Published online (final version): November 29, 2025

https://doi.org/10.33044/revuma.4943

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Abstract

We prove that $\operatorname{vol}(S^{d})/8$ is the highest volume of a pair of $d$-dimensional isospectral and non-isometric spherical orbifolds for any $d\geq5$. Furthermore, we show that $\operatorname{vol}(S^{2n-1})/11$ is the highest volume of a pair of $(2n-1)$-dimensional isospectral and non-isometric spherical space forms if either $n\geq11$ and $n\equiv 1\pmod 5$, or $n\geq7$ and $n\equiv 2\pmod 5$, or $n\geq3$ and $n\equiv 3\pmod 5$.

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