A domain with non-plurisubharmonic $d$-balanced squeezing function

TL;DR

This paper presents an example of a domain where the $d$-balanced squeezing function is not plurisubharmonic, challenging assumptions about its regularity properties.

Contribution

It provides the first known example demonstrating that the $d$-balanced squeezing function can be non-plurisubharmonic.

Findings

The domain's $d$-balanced squeezing function is non-plurisubharmonic.

This example challenges previous beliefs about the regularity of the squeezing function.

It advances understanding of the geometric properties of complex domains.

Abstract

In this note, we give an example of a domain whose $d$-balanced squeezing function is non-plurisubharmonic.