Equidistribution of expanding translates of smooth curves in homogeneous spaces under the action of a product of SO(n,1)'s
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917067241816064 |
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| author | Shin, Yubin |
| author_facet | Shin, Yubin |
| contents | We study the limiting distributions of expanding translates of a compact segment of a smooth curve under a diagonal subgroup of $G=\mathrm{SO}(n_1,1)\times\cdots\times\mathrm{SO}(n_k,1)$, where $G$ acts on a finite volume homogeneous space $L/Γ$ as a subgroup. We show that the expanding translates of the curve become equidistributed in the orbit closure of $G$, provided that Lebesgue almost every point on the curve avoids a certain countable collection of algebraic obstructions. The proof involves Ratner's measure classification theorem, Kempf's geometric invariant theory, and the linearization technique. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_04799 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equidistribution of expanding translates of smooth curves in homogeneous spaces under the action of a product of SO(n,1)'s Shin, Yubin Dynamical Systems 37A17 22E40 37A17 (Primary) 22E40, 37D40 (Secondary) We study the limiting distributions of expanding translates of a compact segment of a smooth curve under a diagonal subgroup of $G=\mathrm{SO}(n_1,1)\times\cdots\times\mathrm{SO}(n_k,1)$, where $G$ acts on a finite volume homogeneous space $L/Γ$ as a subgroup. We show that the expanding translates of the curve become equidistributed in the orbit closure of $G$, provided that Lebesgue almost every point on the curve avoids a certain countable collection of algebraic obstructions. The proof involves Ratner's measure classification theorem, Kempf's geometric invariant theory, and the linearization technique. |
| title | Equidistribution of expanding translates of smooth curves in homogeneous spaces under the action of a product of SO(n,1)'s |
| topic | Dynamical Systems 37A17 22E40 37A17 (Primary) 22E40, 37D40 (Secondary) |
| url | https://arxiv.org/abs/2511.04799 |