Metric stability of trees and tight spans

被引：2

作者：

Lang, Urs ^{[1
]}

Pavon, Mael ^{[1
]}

Zuest, Roger ^{[2
]}

机构：

[1] ETH, Dept Math, CH-8092 Zurich, Switzerland

[2] Univ Fribourg, Dept Math, CH-1700 Fribourg, Switzerland

来源：

ARCHIV DER MATHEMATIK | 2013年 / 101卷 / 01期

基金：

瑞士国家科学基金会;

关键词：

Gromov-Hausdorff distance; Injective hull; Tight span; Metric tree; SPACES;

D O I：

10.1007/s00013-013-0535-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove optimal extension results for roughly isometric relations between metric (-)trees and injective metric spaces. This yields sharp stability estimates, in terms of the Gromov-Hausdorff (GH) distance, for certain metric spanning constructions: the GH distance of two metric trees spanned by some subsets is smaller than or equal to the GH distance of these sets. The GH distance of the injective hulls, or tight spans, of two metric spaces is at most twice the GH distance between themselves.

引用

页码：91 / 100

页数：10

共 31 条

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