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

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.

### 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.)
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