32 citations · 140 across the 39 of their papers we have counts for
19 papers · 1 filter
Variational problems concerning length distances in metric spaces
Fares Essebei, Enrico Pasqualetto
Given a locally compact, complete metric space and an open set , we study the class of length distances on that are bounded from…
Topological regularity of isoperimetric sets in PI spaces having a deformation property
Gioacchino Antonelli, Enrico Pasqualetto, Marco Pozzetta +1
We prove topological regularity results for isoperimetric sets in PI spaces having a suitable deformation property, which prescribes a control on the increment of the perimeter of…
The Rank-One Theorem on spaces
Gioacchino Antonelli, Camillo Brena, Enrico Pasqualetto
We extend Alberti's Rank-One Theorem to metric measure spaces.
Pullback of a quasiconformal map between arbitrary metric measure spaces
Toni Ikonen, Danka Lučić, Enrico Pasqualetto
We prove that every (geometrically) quasiconformal homeomorphism between metric measure spaces induces an isomorphism between the cotangent modules constructed by Gigli. We obtain…
Non-Hilbertian tangents to Hilbertian spaces
Danka Lučić, Enrico Pasqualetto, Tapio Rajala
We provide examples of infinitesimally Hilbertian, rectifiable, Ahlfors regular metric measure spaces having pmGH-tangents that are not infinitesimally Hilbertian.
Constancy of the dimension in codimension one and locality of the unit normal on spaces
Elia Bruè, Enrico Pasqualetto, Daniele Semola
The aim of this paper is threefold. We first prove that, on spaces, the boundary measure of any set with finite perimeter is concentrated on the -regular set…
On master test plans for the space of BV functions
Francesco Nobili, Enrico Pasqualetto, Timo Schultz
We prove that on an arbitrary metric measure space a countable collection of test plans is sufficient to recover all functions and their total variation measures. In the s…
Decomposition of integral metric currents
Paolo Bonicatto, Giacomo Del Nin, Enrico Pasqualetto
In the setting of complete metric spaces, we prove that integral currents can be decomposed as a sum of indecomposable components. In the special case of one-dimensional integral c…
Ultralimits of pointed metric measure spaces
Enrico Pasqualetto, Timo Schultz
The aim of this paper is to study ultralimits of pointed metric measure spaces (possibly unbounded and having infinite mass). We prove that ultralimits exist under mild assumptions…
Gamma-convergence of Cheeger energies with respect to increasing distances
Danka Lučić, Enrico Pasqualetto
We prove a -convergence result for Cheeger energies along sequences of metric measure spaces, where the measure space is kept fixed, while distances are monotonically converging…
Direct limits of infinite-dimensional Carnot groups
Terhi Moisala, Enrico Pasqualetto
We give a construction of direct limits in the category of complete metric scalable groups and provide sufficient conditions for the limit to be an infinite-dimensional Carnot grou…
Abstract and concrete tangent modules on Lipschitz differentiability spaces
Toni Ikonen, Enrico Pasqualetto, Elefterios Soultanis
We construct an isometric embedding from Gigli's abstract tangent module into the concrete tangent module of a space admitting a (weak) Lipschitz differentiable structure, and give…
Rectifiability of RCD(K,N) spaces via -splitting maps
Elia Bruè, Enrico Pasqualetto, Daniele Semola
In this note we give new proofs of rectifiability of RCD(K,N) spaces as metric measure spaces and lower semicontinuity of the essential dimension, via -splitting maps. The argum…
Universal infinitesimal Hilbertianity of sub-Riemannian manifolds
Enrico Le Donne, Danka Lučić, Enrico Pasqualetto
We prove that sub-Riemannian manifolds are infinitesimally Hilbertian (i.e., the associated Sobolev space is Hilbert) when equipped with an arbitrary Radon measure. The result foll…
Rectifiability of the reduced boundary for sets of finite perimeter over RCD spaces
Elia Bruè, Enrico Pasqualetto, Daniele Semola
This note is devoted to the study of sets of finite perimeter over RCD metric measure spaces. Its aim is to complete the picture about the generalization of De Giorgi's theo…
Indecomposable sets of finite perimeter in doubling metric measure spaces
Paolo Bonicatto, Enrico Pasqualetto, Tapio Rajala
We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak -Poincaré inequality. Th…
Sharp estimate on the inner distance in planar domains
Danka Lučić, Enrico Pasqualetto, Tapio Rajala
We show that the inner distance inside a bounded planar domain is at most the one-dimensional Hausdorff measure of the boundary of the domain. We prove this sharp result by establi…
Infinitesimal Hilbertianity of locally CAT()-spaces
Simone Di Marino, Nicola Gigli, Enrico Pasqualetto +1
We show that, given a metric space of curvature bounded from above in the sense of Alexandrov, and a positive Radon measure on giving finite mass to bounded sets, t…
On the notion of parallel transport on spaces
Nicola Gigli, Enrico Pasqualetto
We propose a general notion of parallel transport on spaces, prove an unconditioned uniqueness result and existence under suitable assumptions on the space.