EXPLICIT GEODESICS IN GROMOV-HAUSDORFF SPACE

被引：11

作者：

Chowdhury, Samir ^{[1
]}

Memoli, Facundo ^{[1
]}

机构：

[1] Ohio State Univ, Dept Math, 100 Math Tower,231 West 18th Ave, Columbus, OH 43210 USA

来源：

ELECTRONIC RESEARCH ANNOUNCEMENTS IN MATHEMATICAL SCIENCES | 2018年 / 25卷

关键词：

Gromov-Hausdorff distance; geodesics; branching;

D O I：

10.3934/era.2018.25.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide an alternative, constructive proof that the collection M of isometry classes of compact metric spaces endowed with the Cromov-Hausdorff distance is a geodesic space. The core of our proof is a construction of explicit geodesics on M. We also provide several interesting examples of geodesics on M, including a geodesic between S-0 and S-n for any n >= 1.

引用

页码：48 / 59

页数：12

共 50 条

[31] Some Properties of Gromov-Hausdorff Distances
Memoli, Facundo
DISCRETE & COMPUTATIONAL GEOMETRY, 2012, 48 (02) : 416 - 440
[32] The Gromov-Hausdorff distance between spheres
Lim, Sunhyuk
Memoli, Facundo
Smith, Zane
GEOMETRY & TOPOLOGY, 2023, 27 (09) : 3733 - 3800
[33] Gromov-Hausdorff limits in definable families
Bernig, A
ILLINOIS JOURNAL OF MATHEMATICS, 2005, 49 (02) : 475 - 485
[34] A Lorentzian Gromov-Hausdorff notion of distance
Noldus, J
CLASSICAL AND QUANTUM GRAVITY, 2004, 21 (04) : 839 - 850
[35] NONCOMMUTATIVE SOLENOIDS AND THE GROMOV-HAUSDORFF PROPINQUITY
Latremoliere, Frederic m
Packer, Judith
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145 (05) : 2043 - 2057
[36] Gromov-Hausdorff convergence of quantised intervals
Gotfredsen, Thomas
Kaad, Jens
Kyed, David
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 500 (02)
[37] GROMOV-HAUSDORFF STABILITY FOR GROUP ACTIONS
Dong, Meihua
Lee, Keonhee
Morales, Carlos
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2021, 41 (03) : 1347 - 1357
[38] A continuity criterion for Steiner-type ratios in the Gromov-Hausdorff space
A. S. Pakhomova
Mathematical Notes, 2014, 96 : 130 - 139
[39] Hausdorff and Gromov-Hausdorff Stable Subsets of the Medial Axis
Lieutier, Andre
Wintraecken, Mathijs
PROCEEDINGS OF THE 55TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING, STOC 2023, 2023, : 1768 - 1776
[40] Matricial quantum Gromov-Hausdorff distance
Kerr, D
JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 205 (01) : 132 - 167

← 1 2 3 4 5 →