Generalized small cancellation conditions, non-positive curvature and diagrammatic reducibility

of non-positive Gaussian curvature

A note on quasi-positive curvature conditions

Article history: Received 10 July 2013 Available online 17 April 2014 Communicated by D.V. Alekseevsky MSC: primary 53C21 secondary 53C20 We classify the triples H ⊂ K ⊂ G of nested compact Lie groups which satisfy the “positive triple” condition that was shown in [17] to ensure that G/H admits a metric with quasi-positive curvature. A few new examples of spaces that admit quasi-positively curv...

Non-linear ergodic theorems in complete non-positive curvature metric spaces

Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...

Dehn Functions and Non-Positive Curvature

Semirecursive Sets and Positive Reducibility