A Stefan-Sussmann theorem for normal distributions on manifolds with boundary

TL;DR

This paper extends the Stefan-Sussmann theorem to manifolds with boundary for normal distributions, introducing neat integral manifolds with boundary and establishing conditions for their existence.

Contribution

It provides a new version of the Stefan-Sussmann theorem applicable to manifolds with boundary, involving neat integral manifolds with boundary and adapted collar conditions.

Findings

Normal distributions contain vectors transverse to the boundary.

Plain integral manifolds are insufficient for integration.

Conditions for integrability involve adapted collars and boundary distributions.

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.