Note on explicit proof of Poincare inequality for differential forms on manifolds

TL;DR

This paper establishes a Poincare inequality for differential forms on compact manifolds by extending local inequalities on convex sets to a global setting.

Contribution

It provides a constructive method to globalize local Poincare inequalities for differential forms on manifolds.

Findings

Proved a Poincare inequality for differential forms on compact manifolds.

Developed a constructive globalization technique for local inequalities.

Enhanced understanding of inequalities on differential forms in geometric analysis.

Abstract

We prove a Poincare type inequality for differential forms on compact manifolds by means of a constructive 'globalization' of a local Poincare inequality on convex sets.