Weak {$q$}-concavity conditions for {$CR$}-manifolds

TL;DR

This paper introduces new notions of q-pseudo-concavity for CR manifolds and explores their implications for hypoellipticity, maximum modulus principles, and Cauchy problems in CR function theory.

Contribution

It develops novel q-pseudo-concavity conditions for CR manifolds and applies them to fundamental problems in CR analysis.

Findings

Established links between q-pseudo-concavity and hypoellipticity

Derived maximum modulus principles under new concavity conditions

Analyzed Cauchy problems using the introduced notions

Abstract

We introduce various notions of q-pseudo-concavity for abstract CR manifolds and we apply these notions to the study of hyoo-ellipticity, maximum modulus principle and Cauchy problems for CR functions.