552 citations · 2k across the 45 of their papers we have counts for
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A differential perspective on Gradient Flows on -spaces and applications
Nicola Gigli, Francesco Nobili
We review the theory of Gradient Flows in the framework of convex and lower semicontinuous functionals on -spaces and prove that they can be characterized by the same…
Partial derivatives in the nonsmooth setting
Nicola Gigli, Chiara Rigoni
We study partial derivatives on the product of two metric measure structures, in particular in connection with calculus via modules as proposed by the first named author. Our main…
Global Lipschitz extension preserving local constants
Simone Di Marino, Nicola Gigli, Aldo Pratelli
The intent of this short note is to extend real valued Lipschitz functions on metric spaces, while locally preserving the asymptotic Lipschitz constant. We then apply this results…
Displacement convexity of Entropy and the distance cost Optimal Transportation
Fabio Cavalletti, Nicola Gigli, Flavia Santarcangelo
During the last decade Optimal Transport had a relevant role in the study of geometry of singular spaces that culminated with the Lott-Sturm-Villani theory. The latter is built on…
Korevaar-Schoen's energy on strongly rectifiable spaces
Nicola Gigli, Alexander Tyulenev
We extend Korevaar-Schoen's theory of metric valued Sobolev maps to cover the case of the source space being an RCD space. In this situation it appears that no version of the `subp…