552 citations · 2k across the 45 of their papers we have counts for
7 papers · 1 filter
Infinitesimal Hilbertianity of locally CAT()-spaces
Simone Di Marino, Nicola Gigli, Enrico Pasqualetto +1
We show that, given a metric space of curvature bounded from above in the sense of Alexandrov, and a positive Radon measure on giving finite mass to bounded sets, t…
Differential of metric valued Sobolev maps
Nicola Gigli, Enrico Pasqualetto, Elefterios Soultanis
We introduce a notion of differential of a Sobolev map between metric spaces. The differential is given in the framework of tangent and cotangent modules of metric measure spaces,…
Second order differentiation formula on spaces
Nicola Gigli, Luca Tamanini
We prove the second order differentiation formula along geodesics in finite-dimensional spaces. Our approach strongly relies on the approximation of -geodesics by e…
Differential structure associated to axiomatic Sobolev spaces
Nicola Gigli, Enrico Pasqualetto
The aim of this note is to explain in which sense an axiomatic Sobolev space over a general metric measure space (à la Gol'dshtein-Troyanov) induces - under suitable locality assum…
Benamou-Brenier and duality formulas for the entropic cost on spaces
Nicola Gigli, Luca Tamanini
In this paper we prove that, within the framework of spaces with , the entropic cost (i.e. the minimal value of the Schrödinger problem) admits: - a threef…
On the notion of parallel transport on spaces
Nicola Gigli, Enrico Pasqualetto
We propose a general notion of parallel transport on spaces, prove an unconditioned uniqueness result and existence under suitable assumptions on the space.