LIMITING BEHAVIOR OF THE KOBAYASHI DISTANCE

Given a sequence {Dm } of bounded and convex domains in a complex Banach space, we describe the limiting behavior of the corresponding sequence {k D m } of Kobayashi distances when the given sequence {Dm } is either monotonic or convergent in the Hausdorff metric. 2010Mathematics Subject Classificat...

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Published inTaiwanese journal of mathematics Vol. 19; no. 2; pp. 535 - 552
Main Authors Budzyńska, Monika, Kuczumow, Tadeusz, Reich, Simeon
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.04.2015
Subjects
Banach space
Increasing sequences
Infinity
Mathematical functions
Mathematical theorems
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ISSN1027-5487
2224-6851
DOI10.11650/tjm.19.2015.4719

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Summary:Given a sequence {Dm } of bounded and convex domains in a complex Banach space, we describe the limiting behavior of the corresponding sequence {k D m } of Kobayashi distances when the given sequence {Dm } is either monotonic or convergent in the Hausdorff metric. 2010Mathematics Subject Classification: 32A10, 32F45, 46G20, 46T25. Key words and phrases: Hausdorff metric, Holomorphic mapping, Kobayashi distance, Monotonic sequences of bounded and convex domains.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.19.2015.4719