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On the sub-quadratic isoperimetric inequality. (English) Zbl 0849.20026

Charney, Ruth (ed.) et al., Geometric group theory. Proceedings of a special research quarter at The Ohio State University, Columbus, OH, USA., spring 1992. Berlin: de Gruyter. Ohio State Univ. Math. Res. Inst. Publ. 3, 149-157 (1995).
The author gives a combinatorial proof of a well known result of M. Gromov [Hyperbolic groups, Publ., Math. Sci. Res. Inst. 8, 75-263 (1987; Zbl 0634.20015), Sect. 6] that a group satisfying a subquadratic isoperimetric inequality is hyperbolic. In fact, instead of Gromov’s analytic arguments, the author proves that if geodesics diverge in a geodesic metric space then they diverge exponentially (and hence the space is hyperbolic).
For the entire collection see [Zbl 0829.00019].

MSC:

20F65 Geometric group theory
53C22 Geodesics in global differential geometry
53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces

Citations:

Zbl 0634.20015
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