Global homotopy formulas on q-concave CR manifolds for large degrees

TL;DR

This paper develops a global homotopy formula for the tangential Cauchy-Riemann operator on q-concave CR manifolds in large degrees, utilizing functional analysis and approximation techniques to extend local formulas.

Contribution

It introduces a method to derive global homotopy formulas from local ones without regularity loss, applicable to large degree forms on q-concave CR manifolds.

Findings

Established a global homotopy formula for large degrees

Extended local homotopy formulas to a global setting

Maintained regularity in the approximation process

Abstract

Using functional analysis and a Friedrichs approximation lemma for first order differential operators, we derive a global homotopy formula in large degrees for the tangential Cauchy-Riemann operator from local homotopy formulas without loss of regularity.