On the integration of L0-Banach L0-modules and its applications to vector calculus on RCD spaces
Abstract
A finite-dimensional RCD space can be foliated into sufficiently regular leaves, where a differential calculus can be performed. Two important examples are given by the measure-theoretic boundary of the superlevel set of a function of bounded variation and the needle decomposition associated to a Lipschitz function. The aim of this paper is to connect the vector calculus on the lower dimensional leaves with the one on the base space. In order to achieve this goal, we develop a general theory of integration of L0-Banach L0-modules of independent interest. Roughly speaking, we study how to ‘patch together’ vector fields defined on the leaves that are measurable with respect to the foliation parameter.
Main Authors
Format
Articles
Research article
Published
2024
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202405153607Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
1139-1138
DOI
https://doi.org/10.1007/s13163-024-00491-8
Language
English
Published in
Revista Matemática Complutense
Citation
- Caputo, E., Lučić, M., Pasqualetto, E., & Vojnović, I. (2024). On the integration of L0-Banach L0-modules and its applications to vector calculus on RCD spaces. Revista Matemática Complutense, Early online. https://doi.org/10.1007/s13163-024-00491-8
License
Funder(s)
Research Council of Finland
Funding program(s)
Academy Project, AoF
Akatemiahanke, SA
Additional information about funding
E.C. acknowledges the support from the Academy of Finland, grants no. 314789 and 321896. M. L. and I. V. gratefully acknowledge the financial support of the Ministry of Science, Technological Development and Innovation of the Republic of Serbia (Grants No. 451-03-66/2024-03/ 200125 & 451-03-65/2024-03/200125).
Copyright© The Author(s) 2024