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

2021/09/10 by Perrella, David, Pfefferlé, David, Stoyanov, Luchezar
#58A30 (Primary) 53C12 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.04845

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.

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