552 citations · 2k across the 45 of their papers we have counts for
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Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
Nicola Gigli, Andrea Mondino, Giuseppe Savaré
Aim of this paper is to discuss convergence of pointed metric measure spaces in absence of any compactness condition. We propose various definitions, show that all of them are equi…
An overview on the proof of the splitting theorem in non-smooth context
Nicola Gigli
We give a quite detailed overview on the proof of the Cheeger-Colding-Gromoll splitting theorem in the abstract framework of spaces with Riemannian Ricci curvature bounded from bel…
Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from below
Nicola Gigli, Tapio Rajala, Karl-Theodor Sturm
We prove existence and uniqueness of optimal maps on spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result na…
Euclidean spaces as weak tangents of infinitesimally Hilbertian metric spaces with Ricci curvature bounded below
Nicola Gigli, Andrea Mondino, Tapio Rajala
We show that in any infinitesimally Hilbertian -space at almost every point there exists a Euclidean weak tangent, i.e. there exists a sequence of dilations of the space…
The splitting theorem in non-smooth context
Nicola Gigli
We prove that an infinitesimally Hilbertian CD(0,N) space containing a line splits as the product of and an infinitesimally Hilbertian CD(0,N-1) space. By `infinitesimally Hilb…