arXiv math/06121092006-12math.MG

曼哈顿眶褶

Manhattan orbifolds

David Eppstein

备注：: 17 pages, 15 figures. Some definitions and proofs have been revised since the previous version, and a new example has been added
发表信息：: Topology and its Applications 157(2): 494-507, 2009
DOI：: 10.1016/j.topol.2009.10.008

摘要：

本文研究了2-流形上的一类度量，其中除了离散集奇点外，度量局部等距于L_1（或等价于L_infinity）度量，并证明了在一定的附加条件下，这类度量是单射的.我们使用这种结构来找到紧跨度的平方图和相关的图形，我们发现一个内射度量近似的距离在双曲平面类似的方式直线度量近似的欧几里得距离。

英文摘要：

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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