552 citations · 2k across the 45 of their papers we have counts for
8 papers · 1 filter
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…
Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
The aim of the present paper is to bridge the gap between the Bakry-Émery and the Lott-Sturm-Villani approaches to provide synthetic and abstract notions of lower Ricci curvature b…
A Flow Tangent to the Ricci Flow via Heat Kernels and Mass Transport
Nicola Gigli, Carlo Mantegazza
We present a new relation between the short time behavior of the heat flow, the geometry of optimal transport and the Ricci flow. We also show how this relation can be used to defi…
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…
Riemannian Ricci curvature lower bounds in metric measure spaces with -finite measure
Luigi Ambrosio, Nicola Gigli, Andrea Mondino +1
Using techniques of optimal transportation and gradient flows in metric spaces, we extend the notion of Riemannian Curvature Dimension condition introduced (in case…