Peak functions in $\mathbb C$-convex domains

TL;DR

This paper investigates the existence of various peak functions within classes of -convex domains, utilizing a result on the preservation of domain regularity under projection to advance understanding in complex analysis.

Contribution

It demonstrates the existence of different types of peak functions in -convex domains and introduces a method involving the preservation of domain regularity under projection.

Findings

Existence of multiple types of peak functions in -convex domains

A result on preserving regularity of -convex domains under projection

Enhanced understanding of boundary behavior in complex analysis

Abstract

In the paper we show the existence of different types of peak functions in classes of $\mathbb C$-convex domains. As one of tools used in this context is a result on preserving the regularity of $\mathbb C$-convex domains under projection.