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Local convexity properties of balls in Apollonian and Seittenranta's metrics


Author: Riku Klén
Journal: Conform. Geom. Dyn. 17 (2013), 133-144
MSC (2010): Primary 30C65, 51M10, 30F45
DOI: https://doi.org/10.1090/S1088-4173-2013-00257-9
Published electronically: September 10, 2013
MathSciNet review: 3126909
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Abstract: We consider local convexity properties of balls in the Apollonian and Seittenranta's metrics. Balls in the Apollonian metric are considered in the twice punctured space and starlike domains. Balls in Seittenranta's metric are considered in the twice punctured space and in the punctured ball.


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Additional Information

Riku Klén
Affiliation: Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland
Email: riku.klen@utu.fi

DOI: https://doi.org/10.1090/S1088-4173-2013-00257-9
Keywords: Apollonian distance, Seittenranta's distance, metric ball, local convexity
Published electronically: September 10, 2013
Article copyright: © Copyright 2013 American Mathematical Society

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