On the Gromov hyperbolicity of the minimal metric
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911996984688640 |
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| author | Fiacchi, Matteo |
| author_facet | Fiacchi, Matteo |
| contents | In this paper we study the hyperbolicity in the sense of Gromov of domains in $\mathbb{R}^d$ $(d\geq3)$ with respect to the minimal metric introduced by Forstnerič and Kalaj. In particular, we prove that every bounded strongly minimally convex domain is Gromov hyperbolic and its Gromov compactification is equivalent to its Euclindean closure. Moreover, we prove that the boundary of a Gromov hyperbolic convex domain does not contain non-trivial conformal harmonic disks. Finally, we study the relation between the minimal metric and the Hilbert metric in convex domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14742 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Gromov hyperbolicity of the minimal metric Fiacchi, Matteo Complex Variables Differential Geometry Metric Geometry 53C23, 53A10, 32Q45, 30C80, 31A05 In this paper we study the hyperbolicity in the sense of Gromov of domains in $\mathbb{R}^d$ $(d\geq3)$ with respect to the minimal metric introduced by Forstnerič and Kalaj. In particular, we prove that every bounded strongly minimally convex domain is Gromov hyperbolic and its Gromov compactification is equivalent to its Euclindean closure. Moreover, we prove that the boundary of a Gromov hyperbolic convex domain does not contain non-trivial conformal harmonic disks. Finally, we study the relation between the minimal metric and the Hilbert metric in convex domains. |
| title | On the Gromov hyperbolicity of the minimal metric |
| topic | Complex Variables Differential Geometry Metric Geometry 53C23, 53A10, 32Q45, 30C80, 31A05 |
| url | https://arxiv.org/abs/2310.14742 |