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 and the quasihyperbolic balls with small radii are close-to-convex in the punctured space.
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