Remarks on Lempert functions of balanced domains

TL;DR

This paper explores how the properties of invariant functions relate to the geometric convexity of balanced domains, providing insights into their structure and behavior.

Contribution

It clarifies the connection between invariant objects and the geometric convexity of balanced domains, enhancing understanding of their complex structure.

Findings

Invariant objects reflect geometric convexity

Balanced domains exhibit specific behaviors in invariant functions

Results clarify the relationship between geometry and invariants

Abstract

This note should clarify how the behavior of certain invariant objects reflects the geometric convexity of balanced domains.