A domain with non-plurisubharmonic squeezing function

TL;DR

This paper constructs a specific strictly pseudoconvex domain with smooth boundary where the squeezing function fails to be plurisubharmonic, challenging assumptions about the function's properties.

Contribution

It provides the first example of a domain with smooth boundary and strictly pseudoconvexity where the squeezing function is not plurisubharmonic.

Findings

Squeezing function can be non-plurisubharmonic in smooth strictly pseudoconvex domains.

Provides a counterexample to previous conjectures about squeezing functions.

Highlights limitations of plurisubharmonicity in complex domain geometry.

Abstract

We construct a strictly pseudoconvex domain with smooth boundary whose squeezing function is not plurisubharmonic.