On Rational Convexity of Totally Real Sets

TL;DR

This paper establishes a necessary and sufficient condition for the rational convexity of totally real compact sets in complex Euclidean spaces, generalizing classical results and under mild technical assumptions.

Contribution

It provides a new characterization of rational convexity for totally real sets, extending the classical Duval-Sibony theorem under broader conditions.

Findings

Characterization of rational convexity for totally real sets

Generalization of Duval-Sibony's classical result

Applicable under mild technical assumptions

Abstract

Under a mild technical assumption, we prove a necessary and sufficient condition for a totally real compacdt set in $\mathbb{C}^n$ to be rationally convex. This generalizes a classical result of Duval-Sibony