2 citations · 3 across the 15 of their papers we have counts for
15 papers
Planar lamplighter is not of negative type
Gioacchino Antonelli, Emanuele Caputo, Nicola Cavallucci +3
The lamplighter group over the planar integer grid is proved to not be bi-Lipschitz equivalent to any metric space of negative type, so in particular it does not admit a bi-Lipschi…
Sobolev-to-Lipschitz property of geodesically complete spaces with curvature bounded from above
Emanuele Caputo, Nicola Cavallucci, Toni Ikonen
We prove that every length space with curvature bounded from above that is geodesically complete has the Sobolev-to-Lipschitz property with exponent infinity. That is, every Sobole…
Quantum thermodynamics and semidefinite programming: regularization and algorithms
Emanuele Caputo, Augusto Gerolin, Nataliia Monina +2
We investigate variational problems in quantum thermodynamics at positive temperature, in which admissible states are constrained by prescribed outcomes of a finite set of measurem…
Comparison estimates on nonsmooth spaces with integrable Ricci lower bounds via localization
Emanuele Caputo, Francesco Nobili, Tommaso Rossi
We study comparison estimates on metric measure spaces admitting a synthetic variable Ricci curvature lower bound. We obtain geometric and functional inequalities assuming that the…
A characterization of snowflakes via rectifiability
Emanuele Caputo, Nicola Cavallucci
We prove a generalization of Tyson-Wu's characterization of metric spaces biLipschitz equivalent to snowflakes to every metric space, by removing compactness, doubling and embeddab…
Structure of Metric -currents: approximation by normal currents and representation results
David Bate, Emanuele Caputo, Jakub Takáč +2
We prove the -dimensional flat chain conjecture in any complete and quasiconvex metric space, namely that metric -currents can be approximated in mass by normal -currents.…
Closed BV-extension and -extension sets
Emanuele Caputo, Jesse Koivu, Danka Lučić +1
This paper studies the relations between extendability of different classes of Sobolev and functions from closed sets in general metric measure spaces. Under the ass…
Geometric characterizations of spaces: an overview of some modern techniques
Emanuele Caputo
We survey recent results on the study of metric measure spaces satisfying a Poincaré inequality. We overview recent characterizations in terms of objects of dimension 1, such as pe…
Quantum optimal transport with convex regularization
Emanuele Caputo, Augusto Gerolin, Nataliia Monina +1
The goal of this paper is to settle the study of non-commutative optimal transport problems with convex regularization, in their static and finite-dimensional formulations. We cons…
Sobolev spaces via chains in metric measure spaces
Emanuele Caputo, Nicola Cavallucci
We define the chain Sobolev space on a possibly non-complete metric measure space in terms of chain upper gradients. In this context, -chains are a finite collection o…
A geometric approach to Poincaré inequality and Minkowski content of separating sets
Emanuele Caputo, Nicola Cavallucci
The goal of this paper is to continue the study of the relation between the Poincaré inequality and the lower bounds of Minkowski content of separating sets, initiated in our previ…
Poincaré inequality and energy of separating sets
Emanuele Caputo, Nicola Cavallucci
We study geometric characterizations of the Poincaré inequality in doubling metric measure spaces in terms of properties of separating sets. Given a couple of points and a set sepa…
On the integration of Banach modules and its applications to vector calculus on spaces
Emanuele Caputo, Milica Lučić, Enrico Pasqualetto +1
A finite-dimensional space can be foliated into sufficiently regular leaves, where a differential calculus can be performed. Two important examples are given by the mea…
First-order heat content asymptotics on spaces
Emanuele Caputo, Tommaso Rossi
In this paper, we prove first-order asymptotics on a bounded open set of the heat content when the ambient space is an space, under a regularity condition for the…
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,…