Flats in Spaces with Convex Geodesic Bicombings

• Autorzy: Dominic Descombes , Urs Lang
• Języki publikacji: EN

Abstrakty

EN

In spaces of nonpositive curvature the existence of isometrically embedded flat (hyper)planes is often granted by apparently weaker conditions on large scales.We show that some such results remain valid for metric spaces with non-unique geodesic segments under suitable convexity assumptions on the distance function along distinguished geodesics. The discussion includes, among other things, the Flat Torus Theorem and Gromov’s hyperbolicity criterion referring to embedded planes. This generalizes results of Bowditch for Busemann spaces.

Słowa kluczowe

EN

Nonpositive curvature; Geodesic bicombing; Gromov hyperbolic space; Flat Strip Theorem; FlatTorus Theorem

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2016
• Tom: 4
• Numer: 1

Daty

otrzymano

2015-08-25

zaakceptowano

2016-03-14

online

2016-04-07

Twórcy

autor

Dominic Descombes

• Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland

autor

Urs Lang

• Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland

Identyfikatory

DOI

10.1515/agms-2016-0003