Infinitesimal Hilbertianity of Weighted Riemannian Manifolds
Year of publication
2020
Authors
Lučić, Danka; Pasqualetto, Enrico
Abstract
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.
Show moreOrganizations and authors
Publication type
Publication format
Article
Parent publication type
Journal
Article type
Original article
Audience
ScientificPeer-reviewed
Peer-ReviewedMINEDU's publication type classification code
A1 Journal article (refereed), original researchPublication channel information
Journal
Publisher
Volume
63
Issue
1
Pages
118-140
ISSN
Publication forum
Publication forum level
1
Open access
Open access in the publisher’s service
No
Self-archived
Yes
Other information
Fields of science
Mathematics
Keywords
[object Object],[object Object],[object Object]
Publication country
Canada
Internationality of the publisher
International
Language
English
International co-publication
Yes
Co-publication with a company
No
DOI
10.4153/S0008439519000328
The publication is included in the Ministry of Education and Culture’s Publication data collection
Yes