Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 35, 2010, 493-501

CLOSE-TO-CONVEXITY OF QUASIHYPERBOLIC AND j-METRIC BALLS

Riku Klén

University of Turku, Department of Mathematics
FI-20014 University of Turku, Finland; e-mail: riku.klen 'at' utu.fi

Abstract. We consider close-to-convexity of the metric balls defined by the quasihyperbolic metric and the j-metric. We 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.

2000 Mathematics Subject Classification: Primary 30F45; Secondary 30C65.

Key words: j-metric ball, quasihyperbolic ball, close-to-convex domain, local convexity.

Reference to this article: R. Klén: Close-to-convexity of quasihyperbolic and j-metric balls. Ann. Acad. Sci. Fenn. Math. 35 (2010), 493-501.

Full document as PDF file

doi:10.5186/aasfm.2010.3530

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