32 citations · 140 across the 39 of their papers we have counts for
6 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…
Infinitesimal Hilbertianity of weighted Riemannian manifolds
Danka Lučić, Enrico Pasqualetto
The main result of this paper is the following: any `weighted' Riemannian manifold - i.e. endowed with a generic non-negative Radon measure - is `infinitesimally Hilb…
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,…
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…
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.
The Serre-Swan theorem for normed modules
Danka Lučić, Enrico Pasqualetto
The aim of this note is to analyse the structure of the -normed -modules over a metric measure space. These are a tool that has been introduced by N. Gigli to develop a d…