On the existence of flat planes in spaces of non-positive curvature. (English) Zbl 0840.53033

Bridson, Martin R.

Proc. Am. Math. Soc. 123, No. 1, 223-235 (1995).

The author gives a detailed proof of the existence of a flat plane in suitable CAT(0)-spaces \(X\), notably in the universal cover of a polyhedral space of nonpositive curvature. The resulting criterion of word hyperbolicity of a finitely generated group acting properly cocompactly on \(X\) allows him to give a simple geometric proof of the fact that such groups are characterized by a subquadratic isoperimetric inequality.

Reviewer: M.Katz (Vandœuvre)

MSC:

53C23	Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
20F65	Geometric group theory
53C42	Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)

Keywords:

visibility spaces; Gromov hyperbolic groups; CAT(0)-spaces; subquadratic isoperimetric inequality