Diophantine approximations, large intersections and geodesics in negative curvature
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866929248816594944 |
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| author | Ghosh, Anish Nandi, Debanjan |
| author_facet | Ghosh, Anish Nandi, Debanjan |
| contents | In this paper we prove quantitative results about geodesic approximations to submanifolds in negatively curved spaces. Among the main tools is a new and general Jarník-Besicovitch type theorem in Diophantine approximation. The framework we develop is flexible enough to treat manifolds of variable negative curvature, a variety of geometric targets, and logarithm laws as well as spiraling phenomena in both measure and dimension aspect. Several of the results are new also for manifolds of constant negative sectional curvature. We further establish a large intersection property of Falconer in this context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_01406 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Diophantine approximations, large intersections and geodesics in negative curvature Ghosh, Anish Nandi, Debanjan Metric Geometry Dynamical Systems 37D40(Primary), 53C23(Secondary) In this paper we prove quantitative results about geodesic approximations to submanifolds in negatively curved spaces. Among the main tools is a new and general Jarník-Besicovitch type theorem in Diophantine approximation. The framework we develop is flexible enough to treat manifolds of variable negative curvature, a variety of geometric targets, and logarithm laws as well as spiraling phenomena in both measure and dimension aspect. Several of the results are new also for manifolds of constant negative sectional curvature. We further establish a large intersection property of Falconer in this context. |
| title | Diophantine approximations, large intersections and geodesics in negative curvature |
| topic | Metric Geometry Dynamical Systems 37D40(Primary), 53C23(Secondary) |
| url | https://arxiv.org/abs/1911.01406 |