Isometric Embedding of Busemann Surfaces into $$L_1$$ L 1
| Autor: | Jérémie Chalopin, Victor Chepoi, Guyslain Naves |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Surface (mathematics)
Conjecture Planar straight-line graph Computer Science::Computational Geometry Curvature Theoretical Computer Science Planar graph Combinatorics Distortion (mathematics) symbols.namesake Computational Theory and Mathematics Euclidean geometry symbols Mathematics::Metric Geometry Discrete Mathematics and Combinatorics Non-positive curvature Geometry and Topology Mathematics |
| Zdroj: | Discrete & Computational Geometry. 53:16-37 |
| ISSN: | 1432-0444 0179-5376 |
| DOI: | 10.1007/s00454-014-9643-0 |
| Popis: | In this paper, we prove that any non-positively curved 2-dimensional surface (alias, Busemann surface) is isometrically embeddable into $$L_1$$L1. As a corollary, we obtain that all planar graphs which are 1-skeletons of planar non-positively curved complexes with regular Euclidean polygons as cells are $$L_1$$L1-embeddable with distortion at most $$2$$2. Our results significantly improve and simplify the results of the recent paper by A. Sidiropoulos (Non-positive curvature and the planar embedding conjecture, FOCS (2013)). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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