Manhattan orbifolds

We investigate a class of metrics for 2-manifolds in which, e xcept for a discrete set of singular points, the metric is locally isometric to an L1 (or equivalentlyL∞) metric, and show that with certain additional conditions such metrics are injective. We use this construction to find t he tight span of squaregraphs and related graphs, and we find an injective metric that approximates the distances i n the hyperbolic plane analogously to the way the rectilinear metrics approximate the Euclidean distance.

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