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arXiv · 2310.14742

On the Gromov hyperbolicity of the minimal metric

Matteo Fiacchi
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Abstract

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 Forstneri\v{c} 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.

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Matteo Fiacchi. 2023-10-23. On the Gromov hyperbolicity of the minimal metric. https://doi.org/10.1007/s00209-024-03581-x

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