Local Convexity Properties of Quasihyperbolic Balls in Punctured Space

TL;DR

This paper investigates the local convexity and starlikeness of quasihyperbolic balls in punctured space, providing insights into their geometric properties relevant to metric geometry and analysis.

Contribution

It introduces new results on the convexity and starlikeness of quasihyperbolic balls specifically in punctured space, expanding understanding of their geometric structure.

Findings

Quasihyperbolic balls exhibit specific convexity properties in punctured space.

The paper characterizes conditions under which these balls are convex or starlike.

Results have implications for geometric function theory and metric geometry.

Abstract

This paper deals with local convexity properties of the quasihyperbolic metric in the punctured space. We consider convexity and starlikeness of quasihyperbolic balls.