Poincar\'e lemma and global homotopy formulas with sharp anisotropic H\"older estimates in q-concave CR manifolds

TL;DR

This paper establishes sharp anisotropic H"older estimates for solutions to the tangential Cauchy-Riemann equation on q-concave CR manifolds, both locally and globally in the compact case.

Contribution

It introduces new sharp anisotropic H"older estimates for the tangential Cauchy-Riemann equation on q-concave CR manifolds, extending to global solutions on compact manifolds.

Findings

Sharp anisotropic H"older estimates for local solutions

Global estimates for solutions on compact manifolds

Extension of estimates to q-concave CR manifolds

Abstract

We prove sharp anisotropic H\"older estimates for the local solutions of the tangential Cauchy-Riemann equation in q-concave CR manifolds and we derive the same kind of estimates for global solutions when the manifold is compact.