Isospectral spherical space forms and orbifolds of highest volume
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915136679182336 |
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| author | Álzaga, Alfredo Lauret, Emilio A. |
| author_facet | Álzaga, Alfredo Lauret, Emilio A. |
| contents | 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 $n\equiv 3\pmod 5$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_02213 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isospectral spherical space forms and orbifolds of highest volume Álzaga, Alfredo Lauret, Emilio A. Differential Geometry 58J53 (Primary) 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 $n\equiv 3\pmod 5$. |
| title | Isospectral spherical space forms and orbifolds of highest volume |
| topic | Differential Geometry 58J53 (Primary) |
| url | https://arxiv.org/abs/2409.02213 |