10 papers
A categorical perspective on extended metric-topological spaces
Enrico Pasqualetto, Timo Schultz, Janne Taipalus
Motivated by the analysis and geometry of metric-measure structures in infinite dimensions, we study the category of extended metric-topological spaces, along with many of its dist…
A topological characterization of indecomposable sets of finite perimeter
Paolo Bonicatto, Panu Lahti, Enrico Pasqualetto
We prove that a set of finite perimeter is indecomposable if and only if it is, up to a choice of suitable representative, connected in the 1-fine topology. This gives a topologica…
Preduals of metric BV spaces
Enrico Pasqualetto
We study the predual of the space of functions of bounded variation defined over a metric measure space with finite. More specifically…
Metric Sobolev spaces II: dual energies and divergence measures
Luigi Ambrosio, Toni Ikonen, Danka Lučić +1
This is the second of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several approaches to vector calculus in th…
Spaces with Riemannian curvature bounds are universally infinitesimally Hilbertian
Jesús Núñez-Zimbrón, Enrico Pasqualetto, Elefterios Soultanis
We show that a metric space that, at every point, has a Gromov-Hausdorff tangent with the splitting property (i.e. every geodesic line splits off a factor ), is uni…
Tensor products of measurable Banach bundles
Milica Caković, Danka Lučić, Enrico Pasqualetto
We study injective and projective tensor products of measurable Banach bundles. More precisely, given two separable measurable Banach bundles , defined over a pr…