Tangential category and critical point theory

TL;DR

This paper extends the classical relationship between category and critical points to foliations, introducing a weaker Palais-Smale condition to improve critical point results in the context of tangential category.

Contribution

It adapts the classical Ljusternik-Schnirelmann theory to the setting of foliations by defining a weaker Palais-Smale condition for tangential category.

Findings

Established an upper bound of tangential category by critical points.

Introduced a weaker Palais-Smale condition for foliations.

Improved classical critical point theorems for foliated structures.

Abstract

Classical Ljusternik-Schnirelmann category is upper bounded by the number of critical points of any bounded from below differentiable functions of Palais-Smale type. Here we achieve an adaptation of this result for the tangential category of foliations. We introduce a weaker type of Palais-Smale function, obtaining a slight improvement in the classical theorem of critical points.