On the Gromov hyperbolicity of the minimal metricFiacchi, Matteo (Avtor) minimal surfacesminimal metrichyperbolic domainGromov hyperbolicityconvex domainHilbert metricIn 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 Euclidean 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.20242024-09-05 07:47:47Neznano20367sl