Sums of CR functions from competing CR structures

TL;DR

This paper characterizes sums of CR functions from competing CR structures in two scenarios, expanding the theory of pluriharmonic boundary values and exploring projective duality, with explicit vector field characterizations.

Contribution

It introduces explicit vector field-based characterizations for sums of CR functions in two scenarios involving conjugate structures and projective duality.

Findings

Characterization for conjugate CR structures in circular domains.

Extension of pluriharmonic boundary value theory.

Explicit conditions using vector fields for dual structures.

Abstract

In this paper we characterize sums of CR functions from competing CR structures in two scenarios. In one scenario the structures are conjugate and we are adding to the theory of pluriharmonic boundary values. In the second scenario the structures are related by projective duality considerations. In both cases we provide explicit vector field-based characterizations for two-dimensional circular domains satisfying natural convexity conditions.