Taut visibility domains are not necessarily Kobayashi complete

TL;DR

This paper demonstrates that in complex analysis, taut visibility domains in higher dimensions can lack Kobayashi completeness, challenging assumptions about their geometric properties.

Contribution

It constructs bounded taut visibility domains in C^n that are not Kobayashi complete, answering a recent open question negatively.

Findings

Existence of bounded taut visibility domains in C^n that are not Kobayashi complete.

Domains have highly regular boundaries except at a single point.

Provides counterexamples to previous conjectures.

Abstract

We answer a question asked recently by Banik in the negative by showing that for each $n\geq 2$, there exists a taut visibility domain in $\mathbb{C}^n$ that is not Kobayashi complete. The domains that we produce are bounded and have boundaries that are very regular away from a single point.