On the geometric structure of currents tangent to smooth distributions
Differential Geometry
2022-11-22 v3 Analysis of PDEs
Abstract
It is well known that a k-dimensional smooth surface in a Euclidean space cannot be tangent to a non-involutive distribution of k-dimensional planes. In this paper we discuss the extension of this statement to weaker notions of surfaces, namely integral and normal currents. We find out that integral currents behave to this regard exactly as smooth surfaces, while the behaviour of normal currents is rather multifaceted. This issue is strictly related to a geometric property of the boundary of currents, which is also discussed in details.
Keywords
Cite
@article{arxiv.1907.07456,
title = {On the geometric structure of currents tangent to smooth distributions},
author = {Giovanni Alberti and Annalisa Massaccesi and Eugene Stepanov},
journal= {arXiv preprint arXiv:1907.07456},
year = {2022}
}