Isometric Embedding of Busemann Surfaces into $$L_1$$L1

@article{Chalopin2015IsometricEO,
  title={Isometric Embedding of Busemann Surfaces into \$\$L\_1\$\$L1},
  author={J{\'e}r{\'e}mie Chalopin and Victor Chepoi and Guyslain Naves},
  journal={Discrete \& Computational Geometry},
  year={2015},
  volume={53},
  pages={16-37}
}
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… Expand

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