Essentially compact foliations that are not compact (Q1769450)

A foliation is called essentially compact if the set of noncompact leaves has zero Lebesgue measure. The author considers the qualitative behaviour of essentially compact foliations that are not compact. He shows the following theorem: There exists a \(C^{\infty}\) essentially compact foliation of a compact manifold such that the closure of the set of noncompact leaves is not a submanifold. Also there exists a \(C^{\infty}\) essentially compact foliation of a compact manifold such that there are nonproper noncompact leaves.