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math.MG2025

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…

math.MG2025

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…

math.MG2025

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.…

math.MG2025

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…

math.MG2025

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…

math.MG2024

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…