20.500.12556/DiRROS-20367-520c2504-5f4d-789c-c205-b44b7fb4f5ba On the Gromov hyperbolicity of the minimal metric 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 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. minimal surfaces minimal metric hyperbolic domain Gromov hyperbolicity convex domain Hilbert metric true false true Angleški jezik Ni določen Neznano 2024-09-05 07:47:47 2024-09-05 07:47:48 2024-09-10 13:59:16 0000-00-00 00:00:00 2024 0 0 20 str. iss. 2, [article no.] 24 Vol. 308 Oct. 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2024-10-01 517.5 0025-5874 10.1007/s00209-024-03581-x 206119939 s00209-024-03581-x.pdf s00209-024-03581-x.pdf 1 0A5979D64343E4A9971E73184AA294C5 8727e50d0bb2554170383512d91b6f6f179e9fa3ce3c794deefcfe31415ea647 d3ef226f-6b39-11ef-b487-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=28628 https://link.springer.com/article/10.1007/s00209-024-03581-x 1 bd03c767-6b39-11ef-b487-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=28627 Inštitut za matematiko, fiziko in mehaniko 0 0 0