Close-to-convexity of quasihyperbolic and $j$-metric balls

Abstract

We will consider close-to-convexity of the metric balls defined by the quasihyperbolic metric and the $j$-metric. We will show that the $j$-metric balls with small radii are close-to-convex in general subdomains of $\Rn$ and the quasihyperbolic balls with small radii are close-to-convex in the punctured space.

12 pages, 2 figures

References in corpus (2)

• Local Convexity Properties of Quasihyperbolic Balls in Punctured Space
• Local Convexity Properties of j-metric Balls

Cited by in corpus (1)

• Quasiconformal maps with bilipschitz or identity boundary values in Banach spaces