Geodesic
An Approach to the Study of Finitely Presented Groups Based on the Notion of Discrete Curvature
Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 568-575

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A sufficient condition for the hyperbolicity of a group presented in terms of generators and defining relations is considered. The condition is formulated in terms of the negativity of a discrete analog of curvature for the Lyndon–van Kampen diagrams over a presentation of a group and is a generalization of the small cancellation condition.
Keywords: finitely presented group, hyperbolic group. 
I. G. Lysenok. An Approach to the Study of Finitely Presented Groups Based on the Notion of Discrete Curvature. Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 568-575. http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a7/
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