552 citations · 2k across the 45 of their papers we have counts for
7 papers · 1 filter
Rigidity for the spectral gap on -spaces
Nicola Gigli, Christian Ketterer, Kazumasa Kuwada +1
We consider a rigidity problem for the spectral gap of the Laplacian on an -space (a metric measure space satisfying the Riemannian curvature-dimension condition) fo…
Non-collapsed spaces with Ricci curvature bounded from below
Guido De Philippis, Nicola Gigli
We propose a definition of non-collapsed space with Ricci curvature bounded from below and we prove the versions of Colding's volume convergence theorem and of Cheeger-Colding dime…
The injectivity radius of Lie manifolds
Paolo Antonini, Guido De Philippis, Nicola Gigli
We prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive
A note about the strong maximum principle on spaces
Nicola Gigli, Chiara Rigoni
We give a quick and direct proof of the strong maximum principle on finite dimensional spaces based on the Laplacian comparison of the squared distance.
Recognizing the flat torus among spaces via the study of the first cohomology group
Nicola Gigli, Chiara Rigoni
We prove that if the dimension of the first cohomology group of a space is , then the space is a flat torus. This generalizes a classical result due to Bochner to t…
Lecture notes on differential calculus on RCD spaces
Nicola Gigli
These are extended notes of the course given by the author at RIMS, Kyoto, in October 2016. The aim is to give a self-contained overview on the recently developed approach to diffe…