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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.04932 |
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| _version_ | 1866909097439264768 |
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| author | Alpert, Hannah |
| author_facet | Alpert, Hannah |
| contents | Consider a closed manifold $M$ with two Riemannian metrics: one hyperbolic metric, and one other metric $g$. What hypotheses on $g$ guarantee that for a given radius $r$, there are balls of radius $r$ in the universal cover of $(M, g)$ with greather-than-hyperbolic volumes? We show that this conclusion holds for all $r \geq 1$ if $(\mathrm{Vol} (M, g))^2$ is less than a small constant times the hyperbolic volume of $M$. This strengthens a theorem of Sabourau and is partial progress toward a conjecture of Guth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04932 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Growth in the universal cover under large simplicial volume Alpert, Hannah Differential Geometry 53C23 Consider a closed manifold $M$ with two Riemannian metrics: one hyperbolic metric, and one other metric $g$. What hypotheses on $g$ guarantee that for a given radius $r$, there are balls of radius $r$ in the universal cover of $(M, g)$ with greather-than-hyperbolic volumes? We show that this conclusion holds for all $r \geq 1$ if $(\mathrm{Vol} (M, g))^2$ is less than a small constant times the hyperbolic volume of $M$. This strengthens a theorem of Sabourau and is partial progress toward a conjecture of Guth. |
| title | Growth in the universal cover under large simplicial volume |
| topic | Differential Geometry 53C23 |
| url | https://arxiv.org/abs/2402.04932 |