Isometric Embedding of Busemann Surfaces into $L_1$ - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2015

Isometric Embedding of Busemann Surfaces into $L_1$

Résumé

In this paper, we prove that any non-positively curved 2-dimensional surface (alias, Busemann surface) is isometrically embeddable into 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 L1-embeddable with distortion at most 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)).
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Dates et versions

hal-02268738 , version 1 (06-10-2023)

Identifiants

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Jérémie Chalopin, Victor Chepoi, Guyslain Naves. Isometric Embedding of Busemann Surfaces into $L_1$. 2023. ⟨hal-02268738⟩
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