On fully nonlinear CR invariant equations on the Heisenberg group

TL;DR

This paper characterizes second order fully nonlinear CR invariant equations on the Heisenberg group, extending Euclidean results, and establishes comparison principles for solutions in bounded domains and punctured balls.

Contribution

It provides a CR analogue of Euclidean fully nonlinear equation characterizations and proves new comparison principles for these equations on the Heisenberg group.

Findings

Characterization of second order fully nonlinear CR invariant equations

Comparison principle for solutions on bounded domains

Comparison principle for solutions on punctured balls

Abstract

In this paper we provide a characterization of second order fully nonlinear CR invariant equations on the Heisenberg group, which is the analogue in the CR setting of the result proved in the Euclidean setting by A. Li and the first author (2003). We also prove a comparison principle for solutions of second order fully nonlinear CR invariant equations defined on bounded domains of the Heisenberg group and a comparison principle for solutions of a family of second order fully nonlinear equations on a punctured ball.