Enrico Pasqualetto

activity

20162026

most citedAsymptotic isoperimetry on non collapsed spaces with lower Ricci bounds

32 citations · 140 across the 39 of their papers we have counts for

collaborators

48 papers

math.FA2026

A Bochner-type integration theory for random normed modules

Andrea Kubin, Enrico Pasqualetto

We develop a measure and integration theory for random normed modules. Given a probability space $(X, Σ, m)$ , we introduce and study measures taking values into the s…

math.FA2023

On the integration of Banach modules and its applications to vector calculus on $RCD$ spaces

Emanuele Caputo, Milica Lučić, Enrico Pasqualetto +1

A finite-dimensional $RCD$ space can be foliated into sufficiently regular leaves, where a differential calculus can be performed. Two important examples are given by the mea…

math.FA2023

Projective and injective tensor products of Banach $L^{0}$ -modules

Enrico Pasqualetto

We study projective and injective tensor products of Banach $L^{0}$ -modules over a $σ$ -finite measure space. En route, we extend to Banach $L^{0}$ -modules several technical tools of in…

math.FA2023

An axiomatic theory of normed modules via Riesz spaces

Danka Lučić, Enrico Pasqualetto

We introduce and study an axiomatic theory of $V$ -normed $U$ -modules, where $V$ is a Riesz space and $U$ is an $f$ -algebra; the spaces $U$ and $V$ also have some additional structu…

math.FA2023

Vector calculus on weighted reflexive Banach spaces

Enrico Pasqualetto, Tapio Rajala

We study first-order Sobolev spaces on reflexive Banach spaces via relaxation, test plans, and divergence. We show the equivalence of the different approaches to the Sobolev spaces…

math.FA2023

Maps of bounded variation from PI spaces to metric spaces

Camillo Brena, Francesco Nobili, Enrico Pasqualetto

We study maps of bounded variation defined on a metric measure space and valued into a metric space. Assuming the source space to satisfy a doubling and Poincaré property, we produ…

math.MG2023

Variational problems concerning length distances in metric spaces

Fares Essebei, Enrico Pasqualetto

Given a locally compact, complete metric space $(X, D)$ and an open set $Ω \subseteq X$ , we study the class of length distances $d$ on $Ω$ that are bounded from…

math.MG2023★ 7 cited

Topological regularity of isoperimetric sets in PI spaces having a deformation property

Gioacchino Antonelli, Enrico Pasqualetto, Marco Pozzetta +1

We prove topological regularity results for isoperimetric sets in PI spaces having a suitable deformation property, which prescribes a control on the increment of the perimeter of…

math.FA2022

Sobolev and BV functions on $RCD$ spaces via the short-time behaviour of the heat kernel

Camillo Brena, Enrico Pasqualetto, Andrea Pinamonti

In the setting of finite-dimensional $RCD (K, N)$ spaces, we characterize the $p$ -Sobolev spaces for $p \in (1, \infty)$ and the space of functions of bounded variation in term…

math.FA2022

Limits and colimits in the category of Banach $L^{0}$ -modules

Enrico Pasqualetto

We prove that the category of Banach $L^{0}$ -modules over a given $σ$ -finite measure space is both complete and cocomplete, which means that it admits all small limits and colimits.

math.DG2022★ 32 cited

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 $N$ -dimensional $RCD (K, N)$ spaces…

math.FA2022★ 1 cited

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…

math.FA2022

On the reflexivity properties of Banach bundles and Banach modules

Milica Lučić, Enrico Pasqualetto, Ivana Vojnović

In this paper we investigate some reflexivity-type properties of separable measurable Banach bundles over a $σ$ -finite measure space. Our two main results are the following: - The…

math.MG2022★ 4 cited

The Rank-One Theorem on $RCD$ spaces

Gioacchino Antonelli, Camillo Brena, Enrico Pasqualetto

We extend Alberti's Rank-One Theorem to $RCD (K, N)$ metric measure spaces.

math.FA2022

A short proof of the existence of master test plans

Enrico Pasqualetto

The aim of this brief note is to provide a quick and elementary proof of the following known fact: on a metric measure space whose Sobolev space is separable, there exists a test p…

math.AP2022

Variational problems concerning sub-Finsler metrics in Carnot groups

Fares Essebei, Enrico Pasqualetto

This paper is devoted to the study of geodesic distances defined on a subdomain of a given Carnot group, which are bounded both from above and from below by fixed multiples of the…

math.DG2022★ 1 cited

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…

math.MG2021

Pullback of a quasiconformal map between arbitrary metric measure spaces

Toni Ikonen, Danka Lučić, Enrico Pasqualetto

We prove that every (geometrically) quasiconformal homeomorphism between metric measure spaces induces an isomorphism between the cotangent modules constructed by Gigli. We obtain…

math.MG2021

Non-Hilbertian tangents to Hilbertian spaces

Danka Lučić, Enrico Pasqualetto, Tapio Rajala

We provide examples of infinitesimally Hilbertian, rectifiable, Ahlfors regular metric measure spaces having pmGH-tangents that are not infinitesimally Hilbertian.

math.FA2021

The metric-valued Lebesgue differentiation theorem in measure spaces and its applications

Danka Lučić, Enrico Pasqualetto

We prove a version of the Lebesgue Differentiation Theorem for mappings that are defined on a measure space and take values into a metric space, with respect to the differentiation…

math.MG2021★ 1 cited

Constancy of the dimension in codimension one and locality of the unit normal on $RCD (K, N)$ spaces

Elia Bruè, Enrico Pasqualetto, Daniele Semola

The aim of this paper is threefold. We first prove that, on $RCD (K, N)$ spaces, the boundary measure of any set with finite perimeter is concentrated on the $n$ -regular set…

math.MG2021

On master test plans for the space of BV functions

Francesco Nobili, Enrico Pasqualetto, Timo Schultz

We prove that on an arbitrary metric measure space a countable collection of test plans is sufficient to recover all $BV$ functions and their total variation measures. In the s…

math.FA2021★ 2 cited

Representation theorems for normed modules

Simone Di Marino, Danka Lučić, Enrico Pasqualetto

In this paper we study the structure theory of normed modules, which have been introduced by Gigli. The aim is twofold: to extend von Neumann's theory of liftings to the framework…

math.DG2021★ 2 cited

Parallel transport on non-collapsed $RCD (K, N)$ spaces

Emanuele Caputo, Nicola Gigli, Enrico Pasqualetto

We provide a general theory for parallel transport on non-collapsed $RCD$ spaces obtaining both existence and uniqueness results. Our theory covers the case of geodesics and,…

A Bochner-type integration theory for random normed modules

On the integration of Banach modules and its applications to vector calculus on RCD spaces

Projective and injective tensor products of Banach L0-modules

An axiomatic theory of normed modules via Riesz spaces

Vector calculus on weighted reflexive Banach spaces

Maps of bounded variation from PI spaces to metric spaces

Variational problems concerning length distances in metric spaces

Topological regularity of isoperimetric sets in PI spaces having a deformation property

Sobolev and BV functions on RCD spaces via the short-time behaviour of the heat kernel

Limits and colimits in the category of Banach L0-modules

Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds

Duals and pullbacks of normed modules

On the reflexivity properties of Banach bundles and Banach modules

The Rank-One Theorem on RCD spaces

A short proof of the existence of master test plans

Variational problems concerning sub-Finsler metrics in Carnot groups

Sharp isoperimetric comparison on non-collapsed spaces with lower Ricci bounds

Pullback of a quasiconformal map between arbitrary metric measure spaces

Non-Hilbertian tangents to Hilbertian spaces

The metric-valued Lebesgue differentiation theorem in measure spaces and its applications

Constancy of the dimension in codimension one and locality of the unit normal on RCD(K,N) spaces

On master test plans for the space of BV functions

Representation theorems for normed modules

Parallel transport on non-collapsed RCD(K,N) spaces

On the integration of Banach modules and its applications to vector calculus on $RCD$ spaces

Projective and injective tensor products of Banach $L^{0}$ -modules

Sobolev and BV functions on $RCD$ spaces via the short-time behaviour of the heat kernel

Limits and colimits in the category of Banach $L^{0}$ -modules

The Rank-One Theorem on $RCD$ spaces

Constancy of the dimension in codimension one and locality of the unit normal on $RCD (K, N)$ spaces

Parallel transport on non-collapsed $RCD (K, N)$ spaces