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arXiv · 1308.3181

Isometric embedding of Busemann surfaces into $L_1$

Jérémie Chalopin·Victor Chepoi·Guyslain Naves
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Abstract

In this paper, we prove that any non-positively curved 2-dimensional surface (alias, Busemann surface) is isometrically embeddable into $L_1$. 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 $L_1$-embeddable with distortion at most $2+\pi/2<4$. 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.}}

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Jérémie Chalopin, Victor Chepoi, Guyslain Naves. 2013-08-14. Isometric embedding of Busemann surfaces into $L_1$. https://doi.org/10.1007/s00454-014-9643-0

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