Infinitesimal Hilbertianity of Weighted Riemannian Manifolds
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.
Main Authors
Format
Articles
Research article
Published
2020
Series
Subjects
Publication in research information system
Publisher
Canadian Mathematical Society
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202102081480Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
0008-4395
DOI
https://doi.org/10.4153/S0008439519000328
Language
English
Published in
Canadian Mathematical Bulletin
Citation
- Lučić, D., & Pasqualetto, E. (2020). Infinitesimal Hilbertianity of Weighted Riemannian Manifolds. Canadian Mathematical Bulletin, 63(1), 118-140. https://doi.org/10.4153/S0008439519000328
License
Copyright© Canadian Mathematical Society 2019