UNIFORM APPROXIMATION OF METRICS BY GRAPHS

被引：0

作者：

Burago, Dmitri ^{[1
]}

Ivanov, Sergei ^{[2
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[2] Russian Acad Sci, VA Steklov Math Inst, St Petersburg Dept, St Petersburg 191023, Russia

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2015年 / 143卷 / 03期

关键词：

Metric graph; Gromov-Hausdorff distance;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We say that a metric graph is uniformly bounded if the degrees of all vertices are uniformly bounded and the lengths of edges are pinched between two positive constants; a metric space is approximable by a uniform graph if there is one within a finite Gromov-Hausdorff distance. We show that the Euclidean plane and Gromov hyperbolic geodesic spaces with bounded geometry are approximable by uniform graphs, and pose a number of open problems.

引用

页码：1241 / 1256

页数：16

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