Isometric embedding of Busemann surfaces into $L_1$
Computational Geometry
2022-03-03 v1 Discrete Mathematics
Metric Geometry
Abstract
In this paper, we prove that any non-positively curved 2-dimensional surface (alias, Busemann surface) is isometrically embeddable into . 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 -embeddable with distortion at most . Our results significantly improve and simplify the results of the recent paper {\it A. Sidiropoulos, Non-positive curvature, and the planar embedding conjecture, FOCS 2013.}}
Keywords
Cite
@article{arxiv.1308.3181,
title = {Isometric embedding of Busemann surfaces into $L_1$},
author = {Jérémie Chalopin and Victor Chepoi and Guyslain Naves},
journal= {arXiv preprint arXiv:1308.3181},
year = {2022}
}