552 citations · 2k across the 45 of their papers we have counts for
6 papers · 1 filter
A note about charts built by Eriksson-Bique and Soultanis on metric measure spaces
Luca Gennaioli, Nicola Gigli
This note is motivated by recent studies by Eriksson-Bique and Soultanis about the construction of charts in general metric measure spaces. We analyze their construction and provid…
Duals and pullbacks of normed modules
Nicola Gigli, Danka Lučić, Enrico Pasqualetto
We give a general description of the dual of the pullback of a normed module. Ours is the natural generalization to the context of modules of the well-known fact that the dual of t…
Local vector measures
Camillo Brena, Nicola Gigli
Consider a BV function on a Riemannian manifold. What is its differential? And what about the Hessian of a convex function? These questions have clear answers in terms of (co)vecto…
Calculus and fine properties of functions of bounded variation on RCD spaces
Camillo Brena, Nicola Gigli
We generalize the classical calculus rules satisfied by functions of bounded variation to the framework of RCD spaces. In the infinite dimensional setting we are able to define an…
On the regularity of harmonic maps from to spaces and related results
Nicola Gigli
For an harmonic map from a domain in an space to a space we prove the Lipschitz estimate \[ {\rm Lip}(u|_B…
Viscosity solutions of Hamilton-Jacobi equation in spaces and applications to large deviations
Nicola Gigli, Luca Tamanini, Dario Trevisan
The aim of this paper is twofold. - In the setting of RCD(K,) metric measure spaces, we derive uniform gradient and Laplacian contraction estimates along solutions of the v…