Flats in Spaces with Convex Geodesic Bicombings

Dominic Descombes, and Urs Lang. "Flats in Spaces with Convex Geodesic Bicombings." Analysis and Geometry in Metric Spaces 4.1 (2016): 68-84, electronic only. <http://eudml.org/doc/276898>.

@article{DominicDescombes2016,
abstract = {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.},
author = {Dominic Descombes, Urs Lang},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Nonpositive curvature; Geodesic bicombing; Gromov hyperbolic space; Flat Strip Theorem; Flat Torus Theorem; nonpositive curvature; geodesic bicombing; flat strip theorem; flat torus theorem},
language = {eng},
number = {1},
pages = {68-84, electronic only},
title = {Flats in Spaces with Convex Geodesic Bicombings},
url = {http://eudml.org/doc/276898},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Dominic Descombes
AU - Urs Lang
TI - Flats in Spaces with Convex Geodesic Bicombings
JO - Analysis and Geometry in Metric Spaces
PY - 2016
VL - 4
IS - 1
SP - 68
EP - 84, electronic only
AB - 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.
LA - eng
KW - Nonpositive curvature; Geodesic bicombing; Gromov hyperbolic space; Flat Strip Theorem; Flat Torus Theorem; nonpositive curvature; geodesic bicombing; flat strip theorem; flat torus theorem
UR - http://eudml.org/doc/276898
ER -