Infinitesimal Hilbertianity of Weighted Riemannian Manifolds
Lučić, D., & Pasqualetto, E. (2020). Infinitesimal Hilbertianity of Weighted Riemannian Manifolds. Canadian Mathematical Bulletin, 63(1), 118-140. https://doi.org/10.4153/S0008439519000328
Published inCanadian Mathematical Bulletin
© Canadian Mathematical Society 2019
The main result of this paper is the following: any weighted Riemannian manifold (M,g,𝜇), i.e., a Riemannian manifold (M,g) endowed with a generic non-negative Radon measure 𝜇, is infinitesimally Hilbertian, which means that its associated Sobolev space W1,2(M,g,𝜇) is a Hilbert space. We actually prove a stronger result: the abstract tangent module (à la Gigli) associated with any weighted reversible Finsler manifold (M,F,𝜇) can be isometrically embedded into the space of all measurable sections of the tangent bundle of M that are 2-integrable with respect to 𝜇. By following the same approach, we also prove that all weighted (sub-Riemannian) Carnot groups are infinitesimally Hilbertian.
PublisherCanadian Mathematical Society
Publication in research information system
MetadataShow full item record
Showing items with similar title or keywords.
Le Donne, Enrico; Lučić, Danka; Pasqualetto, Enrico (Springer, 2022)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 follows from an embedding of metric derivations ...
Di Marino, Simone; Lučić, Danka; Pasqualetto, Enrico (Institut de France, 2020)We provide a quick proof of the following known result: the Sobolev space associated with the Euclidean space, endowed with the Euclidean distance and an arbitrary Radon measure, is Hilbert. Our new approach relies upon ...
Capogna, Luca; Citti, Giovanna; Le Donne, Enrico; Ottazzi, Alessandro (Elsevier Masson, 2019)We establish regularity of conformal maps between sub-Riemannian manifolds from regularity of Q-harmonic functions, and in particular we prove a Liouville-type theorem, i.e., 1-quasiconformal maps are smooth in all contact ...
Angulo, Pablo; Faraco, Daniel; Guijarro, Luis; Salo, Mikko (American Mathematical Society, 2020)We analyze the structure of the set of limiting Carleman weights in all conformally flat manifolds, $ 3$-manifolds, and $ 4$-manifolds. In particular we give a new proof of the classification of Euclidean limiting Carleman ...
Krupchyk, Katya; Liimatainen, Tony; Salo, Mikko (Elsevier Inc., 2022)In this article we study the linearized anisotropic Calderón problem on a compact Riemannian manifold with boundary. This problem amounts to showing that products of pairs of harmonic functions of the manifold form a ...