Polyhedral Finsler spaces with locally unique geodesics

Dmitri Burago, Sergei Ivanov

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)343-355
Number of pages13
JournalAdvances in Mathematics
StatePublished - Jul 12 2013

All Science Journal Classification (ASJC) codes

  • General Mathematics


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