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Polyhedral Finsler spaces with locally unique geodesics. / Burago, Dmitri; Ivanov, Sergei.

In: Advances in Mathematics, Vol. 247, 12.07.2013, p. 343-355.

Research output: Contribution to journal › Article › peer-review

Harvard

Burago, D & Ivanov, S 2013, 'Polyhedral Finsler spaces with locally unique geodesics', Advances in Mathematics, vol. 247, pp. 343-355. https://doi.org/10.1016/j.aim.2013.07.007

APA

Burago, D., & Ivanov, S. (2013). Polyhedral Finsler spaces with locally unique geodesics. Advances in Mathematics, 247, 343-355. https://doi.org/10.1016/j.aim.2013.07.007

Vancouver

Burago D, Ivanov S. Polyhedral Finsler spaces with locally unique geodesics. Advances in Mathematics. 2013 Jul 12;247:343-355. https://doi.org/10.1016/j.aim.2013.07.007

Author

Burago, Dmitri ; Ivanov, Sergei. / Polyhedral Finsler spaces with locally unique geodesics. In: Advances in Mathematics. 2013 ; Vol. 247. pp. 343-355.

BibTeX

@article{aa5b5b843ec94a43ae81e70dbbd9a570,
title = "Polyhedral Finsler spaces with locally unique geodesics",
abstract = "We study Finsler PL spaces, that is simplicial complexes glued out of simplices cut off from some normed spaces. We are interested in the class of Finsler PL spaces featuring local uniqueness of geodesics (for complexes made of Euclidean simplices, this property is equivalent to local CAT(0)). Though non-Euclidean normed spaces never satisfy CAT(0), it turns out that they share many common features. In particular, a globalization theorem holds: in a simply-connected Finsler PL space local uniqueness of geodesics implies the global one. However the situation is more delicate here: some basic convexity properties do not extend to the PL Finsler case.",
keywords = "CAT(0), Finsler geometry, Normed spaces, Polyhedral spaces",
author = "Dmitri Burago and Sergei Ivanov",
year = "2013",
month = jul,
day = "12",
doi = "10.1016/j.aim.2013.07.007",
language = "English",
volume = "247",
pages = "343--355",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Polyhedral Finsler spaces with locally unique geodesics

AU - Burago, Dmitri

AU - Ivanov, Sergei

PY - 2013/7/12

Y1 - 2013/7/12

N2 - We study Finsler PL spaces, that is simplicial complexes glued out of simplices cut off from some normed spaces. We are interested in the class of Finsler PL spaces featuring local uniqueness of geodesics (for complexes made of Euclidean simplices, this property is equivalent to local CAT(0)). Though non-Euclidean normed spaces never satisfy CAT(0), it turns out that they share many common features. In particular, a globalization theorem holds: in a simply-connected Finsler PL space local uniqueness of geodesics implies the global one. However the situation is more delicate here: some basic convexity properties do not extend to the PL Finsler case.

AB - We study Finsler PL spaces, that is simplicial complexes glued out of simplices cut off from some normed spaces. We are interested in the class of Finsler PL spaces featuring local uniqueness of geodesics (for complexes made of Euclidean simplices, this property is equivalent to local CAT(0)). Though non-Euclidean normed spaces never satisfy CAT(0), it turns out that they share many common features. In particular, a globalization theorem holds: in a simply-connected Finsler PL space local uniqueness of geodesics implies the global one. However the situation is more delicate here: some basic convexity properties do not extend to the PL Finsler case.

KW - CAT(0)

KW - Finsler geometry

KW - Normed spaces

KW - Polyhedral spaces

UR - http://www.scopus.com/inward/record.url?scp=84882991954&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2013.07.007

DO - 10.1016/j.aim.2013.07.007

M3 - Article

AN - SCOPUS:84882991954

VL - 247

SP - 343

EP - 355

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -

ID: 49983179