English

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

R2 v1 2026-06-23T09:01:03.224Z