On the integration of Banach modules and its applications to vector calculus on ${\sf RCD}$ spaces

Autor:	Caputo, Emanuele, Lučić, Milica, Pasqualetto, Enrico, Vojnović, Ivana
Rok vydání:	2023
Předmět:	Mathematics - Functional Analysis Mathematics - Metric Geometry 28A50 53C23 26A45
Druh dokumentu:	Working Paper
Popis:	A finite-dimensional ${\sf RCD}$ 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 $L^0$-Banach $L^0$-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. Comment: 22 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2308.12042 Zobrazit plný text záznamu View this record from Arxiv