Hyperbolicity and Vitali properties of unbounded domains in Banach spaces

TL;DR

This paper investigates local boundary conditions in unbounded Banach space domains that ensure hyperbolicity and Vitali properties, extending concepts analogous to tautness from finite-dimensional complex analysis.

Contribution

It introduces local boundary conditions in unbounded Banach space domains that guarantee hyperbolicity and Vitali properties, generalizing finite-dimensional tautness concepts.

Findings

Identifies boundary conditions ensuring hyperbolicity in Banach space domains.

Establishes criteria for Vitali properties in unbounded domains.

Extends finite-dimensional complex analysis concepts to infinite-dimensional spaces.

Abstract

Let $\Om$ be a unbounded domain in a Banach space. In this work, we wish to impose {\it local conditions} on boundary point of $\Om$ (including the point at infinity) that guarantee complete hyperbolic of $\Om.$ We also search for local boundary conditions so that Vitali properties hold true for $\Om.$ These properties might be considered as analogues of the taut property in the finite dimensional case.