2021
1.
Perrella, David; Pfefferlé, David; Stoyanov, Luchezar
A Stefan-Sussmann Theorem for Normal Distributions on Manifolds with Boundary Journal Article
In: arXiv:2109.04845 [math], 2021.
Abstract | BibTeX | Tags: differential geometry, foliations, Froebenius, integrability, manifolds, topology
@article{perrellaStefanSussmannTheoremNormal2021,
title = {A Stefan-Sussmann Theorem for Normal Distributions on Manifolds with Boundary},
author = {David Perrella and David Pfefferl\'{e} and Luchezar Stoyanov},
year = {2021},
date = {2021-09-01},
urldate = {2021-09-01},
journal = {arXiv:2109.04845 [math]},
abstract = {An analogue of the Stefan-Sussmann Theorem on manifolds with boundary is proven for normal distributions. These distributions contain vectors transverse to the boundary along its entirety. Plain integral manifolds are not enough to "integrate" a normal distribution; the next best "integrals" are so-called neat integral manifolds with boundary. The conditions on the distribution for this integrability is expressed in terms of adapted collars and integrability of a pulled-back distribution on the interior and on the boundary.},
keywords = {differential geometry, foliations, Froebenius, integrability, manifolds, topology},
pubstate = {published},
tppubtype = {article}
}
An analogue of the Stefan-Sussmann Theorem on manifolds with boundary is proven for normal distributions. These distributions contain vectors transverse to the boundary along its entirety. Plain integral manifolds are not enough to "integrate" a normal distribution; the next best "integrals" are so-called neat integral manifolds with boundary. The conditions on the distribution for this integrability is expressed in terms of adapted collars and integrability of a pulled-back distribution on the interior and on the boundary.