Every bounded pseudoconvex domain with H\"older boundary is hyperconvex

TL;DR

This paper proves that all bounded pseudoconvex domains with H"older continuous boundaries in complex space are hyperconvex, expanding understanding of domain properties in complex analysis.

Contribution

It establishes that H"older boundary regularity implies hyperconvexity for bounded pseudoconvex domains, a previously unconfirmed connection.

Findings

Bounded pseudoconvex domains with H"older boundary are hyperconvex

H"older boundary regularity ensures hyperconvexity in complex domains

Expands the class of domains known to be hyperconvex

Abstract

We show that every bounded pseudoconvex domain with H\"older boundary in $\mathbb C^n$ is hyperconvex.