Year: 2026
Type: preprint
Abstract: This paper is the second in a series by the author and collaborators devoted to the study of geometric and analytic properties of nonlinear Lebesgue spaces, that is, L^p spaces of mappings taking values in arbitrary metric spaces. The present article formalizes the pointwise description of their geometric properties---their length structure, bounds on their Alexandrov curvature as well as the definition of a velocity for absolutely continuous curves despite the lack of differential structure. To obtain this pointwise description, we first prove a nonlinear analogue of the Fubini--Lebesgue theorem, which yields an identification of L^p curves in nonlinear Lebesgue spaces with mappings taking values in the space of L^p curves. This identification of L^p curves then enables a similar identification for absolutely continuous curves, from which the pointwise description of the geometric properties of nonlinear Lebesgue spaces follows.
Source: arXiv (Cornell University)
Author: Sérieys, Guillaume
Institution: Mathématiques Appliquées à Paris 5
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Université Gustave Eiffel
OpenAlex ID: W7134885675