8 papers
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 TakÃ¡Ä +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.…
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…