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. 
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     author = {I. G. Lysenok},
     title = {An {Approach} to the {Study} of {Finitely} {Presented} {Groups} {Based} on the {Notion} of {Discrete} {Curvature}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {568--575},
     publisher = {mathdoc},
     volume = {103},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a7/}
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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/