Bridson, Martin R. On the existence of flat planes in spaces of non-positive curvature. (English) Zbl 0840.53033 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) Cited in 1 ReviewCited in 14 Documents 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 PDF BibTeX XML Cite \textit{M. R. Bridson}, Proc. Am. Math. Soc. 123, No. 1, 223--235 (1995; Zbl 0840.53033) Full Text: DOI OpenURL