32 citations · 140 across the 39 of their papers we have counts for
8 papers · 1 filter
Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds
Gioacchino Antonelli, Enrico Pasqualetto, Marco Pozzetta +1
This paper studies sharp and rigid isoperimetric comparison theorems and asymptotic isoperimetric properties for small and large volumes on -dimensional spaces…
Sharp isoperimetric comparison on non-collapsed spaces with lower Ricci bounds
Gioacchino Antonelli, Enrico Pasqualetto, Marco Pozzetta +1
This paper studies sharp isoperimetric comparison theorems and sharp dimensional concavity properties of the isoperimetric profile for non smooth spaces with lower Ricci curvature…
Parallel transport on non-collapsed spaces
Emanuele Caputo, Nicola Gigli, Enrico Pasqualetto
We provide a general theory for parallel transport on non-collapsed spaces obtaining both existence and uniqueness results. Our theory covers the case of geodesics and,…
Isoperimetric sets in spaces with lower bounds on the Ricci curvature
Gioacchino Antonelli, Enrico Pasqualetto, Marco Pozzetta
In this paper we study regularity and topological properties of volume constrained minimizers of quasi-perimeters in spaces where the reference measure is the Hausdorff m…
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…
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…
Equivalence of two different notions of tangent bundle on rectifiable metric measure spaces
Nicola Gigli, Enrico Pasqualetto
We prove that for a suitable class of metric measure spaces, the abstract notion of tangent module as defined by the first author can be isometrically identified with the space of…
Behaviour of the reference measure on spaces under charts
Nicola Gigli, Enrico Pasqualetto
Mondino and Naber recently proved that finite dimensional spaces are rectifiable. Here we show that the push-forward of the reference measure under the charts built by th…