2 citations · 2 across the 6 of their papers we have counts for
7 papers
Large-scale rank and geometry of the Lipschitz metric on geodesic currents
Dídac Martínez-Granado, Jenya Sapir
For a closed orientable surface of genus at least 2, we study the large-scale geometry of the (symmetrized) Lipschitz metric on its space of projective filling geodesic currents. W…
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…
Comparing hyperbolic and extremal lengths for shortest curves
Dídac Martínez-Granado, Franco Vargas Pallete
We give a lower bound for the widths of the collars of certain short partial pants decomposition of the surface. Then we apply this to obtain upper bounds of the renormalized volum…