1 citations · 1 across the 7 of their papers we have counts for
8 papers
Orientability of metric manifolds and metric spaces with curvature bounds
Nicola Cavallucci, Denis Marti, Andrea Mondino +1
We develop a theory of orientability for metric manifolds and singular metric spaces using locally integral currents. For topological -manifolds with locally finite Hausdorff me…
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…
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…
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…
The Metric Completion of the Space of Vector-Valued One-Forms
Nicola Cavallucci, Zhe Su
The space of full-ranked one-forms on a smooth, orientable, compact manifold (possibly with boundary) is metrically incomplete with respect to the induced geodesic distance of the…