| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4660428 | Topology and its Applications | 2010 | 14 Pages |
Abstract
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 L1 (or equivalently Lā) 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
