Fractional Divisibility of Spheres with Partially Generic Sets of Rotations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912201112027136 |
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| author | Grebík, Jan Ikenmeyer, Christian Pikhurko, Oleg |
| author_facet | Grebík, Jan Ikenmeyer, Christian Pikhurko, Oleg |
| contents | We say that an r-tuple $(g_1,...,g_r)$ of special orthogonal $d\times d$ matrices fractionally divides the $(d-1)$-dimensional sphere $S$ if there is a non-constant function in $L^2(S)$ such that its translations by $g_1,...,g_r$ sum up to the constant-1 function. Our main result shows, informally speaking, that fractional divisibility is impossible if at least $r/2$ rotations are ``generic". |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13522 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional Divisibility of Spheres with Partially Generic Sets of Rotations Grebík, Jan Ikenmeyer, Christian Pikhurko, Oleg Metric Geometry We say that an r-tuple $(g_1,...,g_r)$ of special orthogonal $d\times d$ matrices fractionally divides the $(d-1)$-dimensional sphere $S$ if there is a non-constant function in $L^2(S)$ such that its translations by $g_1,...,g_r$ sum up to the constant-1 function. Our main result shows, informally speaking, that fractional divisibility is impossible if at least $r/2$ rotations are ``generic". |
| title | Fractional Divisibility of Spheres with Partially Generic Sets of Rotations |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2501.13522 |