7 papers · 1 filter
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.…
Closed BV-extension and -extension sets
Emanuele Caputo, Jesse Koivu, Danka LuÄiÄ +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 p…
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…