Weak stationarity of a matrix valued differential form at superdensity points of its vanishing set

TL;DR

This paper proves a property of weak stationarity for matrix-valued differential forms at superdensity points of their zero set and applies this result to the Maurer-Cartan equation.

Contribution

It introduces a new weak stationarity property at superdensity points and applies it to the Maurer-Cartan equation, advancing understanding in differential geometry.

Findings

Weak stationarity property established at superdensity points.

Application of the property to the Maurer-Cartan equation.

Provides new insights into the structure of differential forms.

Abstract

A property of weak stationarity of a matrix valued differential form at superdensity points of its vanishing set is proved. This result is then applied in the context of the Maurer-Cartan equation.