Weak pseudoconcavity and the maximum modulus principle

TL;DR

This paper explores the maximum modulus principle and weak unique continuation for CR functions on almost CR manifolds, focusing on the effects of weak pseudoconcavity and propagation along Sussmann leaves.

Contribution

It provides new sharp results on the propagation of CR functions under weak pseudoconcavity conditions on abstract almost CR manifolds.

Findings

Propagation results along Sussmann leaves

Sharp maximum modulus principles under weak pseudoconcavity

Analysis of weak unique continuation for CR functions

Abstract

We discuss the maximum modulus principle, and weak unique continuation, for CR functions on an abstract almost CR manifold M. We investigate these matters under the assumption of weak pseudoconcavity, and obtain sharp results about propagation along Sussmann leaves.