Manhattan orbifolds

Details Manhattan orbifolds Manhattan orbifolds

2006-12-05

arxiv.org/abs/math/0612109v2

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

Mathematics

Metric Geometry

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

Scientific paper

10.1016/j.topol.2009.10.008

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.

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