On the Gromov hyperbolicity of the minimal metric

Fiacchi, Matteo (author)

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 (Anal PDE 17(3):981–1003, 2024). 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.

• Language: English
• Keywords: minimal surfaces, minimal metric, hyperbolic domain, Gromov hyperbolicity, convex domain, Hilbert metric
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 20 str.
• Numbering: Vol. 308, iss. 2, art. 24
• PID: 20.500.12556/RUL-160783-d8f0da79-0704-76cf-c949-aaf80999d0d6
• UDC: 517.5
• ISSN on article: 0025-5874
• DOI: 10.1007/s00209-024-03581-x
• COBISS.SI-ID: 206119939
• Publication date in RUL: 04.09.2024

Record is a part of a journal

• Title: Mathematische Zeitschrift
• Shortened title: Math. Z.
• Publisher: Springer Nature
• ISSN: 0025-5874
• COBISS.SI-ID: 25915904

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Projects

• Funder: EC - European Commission
• Funding programme: HE
• Project number: 101053085
• Name: Holomorphic Partial Differential Relations
• Acronym: HPDR

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P1-0291
• Name: Analiza in geometrija