4 papers · 1 filter
Convergence of metric measure spaces via embeddings in the Urysohn universal space
Milica Caković, Enrico Pasqualetto, Timo Schultz
We study different notions of convergence of metric measure spaces by means of isometric embeddings into the Urysohn universal metric space . Due to the universality of…
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…
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…
A note on Laplacian bounds, deformation properties and isoperimetric sets in metric measure spaces
Enrico Pasqualetto, Tapio Rajala
In the setting of length PI spaces satisfying a suitable deformation property, it is known that each isoperimetric set has an open representative. In this paper, we construct an ex…