5 papers
Geodesic currents of coarse negative curvature
Meenakshy Jyothis, Dídac Martínez-Granado
Strong hyperbolicity is a coarse notion of negative curvature, stronger than Gromov hyperbolicity, that includes all CAT(-k) metrics for k positive and allows the use of dynamical…
The intersection dual of geodesic currents
Dídac Martínez-Granado, Dylan P. Thurston
Geodesic currents on closed hyperbolic surfaces are measures on the unit tangent bundle invariant under geodesic flow and orientation reversal. Every geodesic current induces a dua…
A geometric correspondence for reparameterizations of geodesic flows
Stephen Cantrell, Dídac Martínez-Granado, Eduardo Reyes
For any non-elementary, torsion-free hyperbolic group, we provide a correspondence between the left-invariant Gromov-hyperbolic metrics on the group that are quasi-isometric to a w…
Horoboundary and rigidity of filling geodesic currents
Meenakshy Jyothis, Dídac Martínez-Granado
We endow the space of projective filling geodesic currents on a closed hyperbolic surface with a natural asymmetric metric extending Thurston's asymmetric metric on Teichmüller spa…
Growth tightness and genericity for word metrics from injective spaces
Lihuang Ding, Dídac Martínez-Granado, Abdul Zalloum
Mapping class groups are known to admit geometric (proper, cobounded) actions on injective spaces. Starting with such an action, and relying only on geometric arguments, we show th…