Mesoscopic curvature and hyperbolicity. (English) Zbl 1006.53036

Fernández, Marisa (ed.) et al., Global differential geometry: the mathematical legacy of Alfred Gray. Proceedings of the international congress on differential geometry held in memory of Professor Alfred Gray, Bilbao, Spain, September 18-23, 2000. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 288, 58-69 (2001).
The author introduces a notion of \(\text{CAT}_\delta (\kappa)\)-spaces mediating between \(\text{CAT} (\kappa)=\text{CAT}_0(\kappa)\) and \(\delta\)-hyperbolicity corresponding to \(\text{CAT}_\delta (-\infty)\). This allows the local-to-global passage in the spirit of Cartan-Hadamard that has proved to be most convenient for applications in combinatorial group theory.
For the entire collection see [Zbl 0980.00033].


53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
53C24 Rigidity results