An example concerning the Theory of Levels for codimension-one foliations

TL;DR

This paper presents an example of a codimension-one foliation that is transversely C^1 but does not satisfy the Local Minimal Set property, highlighting limitations in existing foliation theory.

Contribution

It provides a specific example illustrating a foliation with certain regularity that lacks the Local Minimal Set property, advancing understanding of foliation behaviors.

Findings

Existence of a transversely C^1 codimension-one foliation without the Local Minimal Set property

Demonstrates limitations of certain foliation regularity assumptions

Highlights need for refined criteria in foliation theory

Abstract

We give an example of a codimension-one foliation which is transversely of class C^1 and which does not satisfy the "Local Minimal Set" property.