Exhausting domains of the symmetrized bidisc

TL;DR

This paper demonstrates that the symmetrized bidisc can be approximated by strongly linearly convex domains, revealing the existence of such domains that cannot be exhausted by biholomorphic convex domains.

Contribution

It introduces the concept that the symmetrized bidisc can be exhausted by strongly linearly convex domains, highlighting a new geometric property.

Findings

Symmetrized bidisc can be exhausted by strongly linearly convex domains

Existence of strongly linearly convex domains not exhaustible by biholomorphic convex domains

Advances understanding of complex geometric structures

Abstract

We show that the symmetrized bidisc may be exhausted by strongly linearly convex domains. It shows in particular the existence of a strongly linearly convex domain that cannot be exhausted by domains biholomorphic to convex ones.