Is there a theory of foliations by manifolds with boundary? Particularly, Is there a generalization of the Frobenius theorem and the Stefan-Sussmann theorem in which the leaves are manifolds with boundary?
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2026-02-22 17:54:07.1771782847
Manifolds with boundary and foliations
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Once you assume appropriate boundary conditions, everything is the same as in the theory without boundary.
This preprint and this preprint give Frobenius and Stefan-Sussmann type theorems for manifolds with boundary assuming the distribution is normal: there is a vector in the distribution transverse to the boundary at each point. It is precisely this situation where the leaves have boundary.