On the Gromov hyperbolicity of the minimal metric

被引：0

作者：

Fiacchi, Matteo ^{[1
,2
]}

机构：

[1] Univ Ljubljana, Fac Math & Phys, Jadranska 19, Ljubljana 1000, Slovenia

[2] Inst Math Phys & Mech, Ljubljana 191000, Slovenia

来源：

MATHEMATISCHE ZEITSCHRIFT | 2024年 / 308卷 / 02期

基金：

欧洲研究理事会;

关键词：

Minimal surface; Minimal metric; Hyperbolic domain; Gromov hyperbolicity; Convex domain; Hilbert metric; CONVEX DOMAINS; MAPS;

D O I：

10.1007/s00209-024-03581-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the hyperbolicity in the sense of Gromov of domains in R-d (d >= 3) with respect to the minimal metric introduced by Forstneric 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.

引用

页数：20

共 24 条

[1]

Alarcn A., 2021, SPRINGER MONOGRAPHS, DOI 10.1007/978-3-030-69056-4

[2] Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces [J].