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