arXiv:math/0612109 Abstract

arXiv:math/0612109 [math.MG]Abstract References Reviews Resources

Manhattan orbifolds

Published 2006-12-05, updated 2009-04-15Version 2

We investigate a class of metrics for 2-manifolds in which, except for a discrete set of singular points, the metric is locally isometric to an L_1 (or equivalently L_infinity) metric, and show that with certain additional conditions such metrics are injective. We use this construction to find the tight span of squaregraphs and related graphs, and we find an injective metric that approximates the distances in the hyperbolic plane analogously to the way the rectilinear metrics approximate the Euclidean distance.

Comments: 17 pages, 15 figures. Some definitions and proofs have been revised since the previous version, and a new example has been added

Journal: Topology and its Applications 157(2): 494-507, 2009

DOI: 10.1016/j.topol.2009.10.008

Categories: math.MG

Subjects: 57M50, 57M15

Keywords: manhattan orbifolds, rectilinear metrics approximate, discrete set, singular points, euclidean distance

Tags: journal article

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