552 citations · 2k across the 45 of their papers we have counts for
4 papers · 2 filters
The Abresch-Gromoll inequality in a non-smooth setting
Nicola Gigli, Sunra Mosconi
We prove that the Abresch-Gromoll inequality holds on infinitesimally Hilbertian CD(K,N) spaces in the same form as the one available on smooth Riemannian manifolds.
A PDE approach to nonlinear potential theory in metric measure spaces
Nicola Gigli, Andrea Mondino
We show that the tools recently introduced by the first author in [9] allow to give a PDE description of p-harmonic functions in metric measure setting. Three applications are give…
Gromov-Hausdorff convergence of discrete transportation metrics
Nicola Gigli, Jan Maas
This paper continues the investigation of `Wasserstein-like' transportation distances for probability measures on discrete sets. We prove that the discrete transportation metrics o…
On the differential structure of metric measure spaces and applications
Nicola Gigli
The main goals of this paper are: i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradient…