Open access
Datum
2019-04-09Typ
- Journal Article
Abstract
We establish existence and uniqueness results for conical geodesic bicombings on subsets of normed vector spaces. Concerning existence, we give a first example of a convex geodesic bicombing that is not consistent. Furthermore, we show that under a mild geometric assumption on the norm a conical geodesic bicombing on an open subset of a normed vector space locally consists of linear geodesics. As an application, we obtain by the use of a Cartan–Hadamard type result that if a closed convex subset of a Banach space has non-empty interior, then it admits a unique consistent conical geodesic bicombing, namely the one given by the linear segments. Mehr anzeigen
Persistenter Link
https://doi.org/10.3929/ethz-b-000340286Publikationsstatus
publishedExterne Links
Zeitschrift / Serie
Advances in GeometryBand
Seiten / Artikelnummer
Verlag
De GruyterThema
Nonpositive curvature; Geodesic bicombing; Convex setsOrganisationseinheit
03500 - Lang, Urs / Lang, Urs