A Henstock-Kurzweil type integral on 1 dimensional integral currents
Differential Geometry
2019-05-10 v1 Classical Analysis and ODEs
Abstract
We define a non-absolutely convergent integration on integral currents of dimension 1 in Euclidean space. This integral is closely related to the Henstock-Kurzweil and Pfeffer Integrals. Using it, we prove a generalized Fundamental Theorem of Calculus on these currents. A detailed presentation of Henstock-Kurzweil Integration is given in order to make the paper accessible to non-specialists.
Keywords
Cite
@article{arxiv.1905.03382,
title = {A Henstock-Kurzweil type integral on 1 dimensional integral currents},
author = {Antoine Julia},
journal= {arXiv preprint arXiv:1905.03382},
year = {2019}
}
Comments
37 pages, 5 figures