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On the Gromov hyperbolicity of the minimal metric
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Fiacchi, Matteo
(
Author
)
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https://link.springer.com/article/10.1007/s00209-024-03581-x
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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 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
Views:
45
Downloads:
12
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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
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