On Nonuniqueness of Geodesics and Geodesic Disks in the Universal Asymptotic Teichmiiller Space

Abstract The non-uniqueness on geodesics and geodesic disks in the universal asymptotic Teichmfiller space AT（D） are studied in this paper. It is proved that if # is asymptotically extremal in [[#]] with h （μ） 〈 h＊ （μ） for some point ζ∈D, then there exist infinitely many geodesic segments joining [[...

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Bibliographic Details
Published in:数学学报：英文版 2017, Vol.33 (2), p.201-209
Main Author: Yi QI Yan WU
Format: Article
Language:English
Online Access:Get full text
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Summary:Abstract The non-uniqueness on geodesics and geodesic disks in the universal asymptotic Teichmfiller space AT（D） are studied in this paper. It is proved that if # is asymptotically extremal in [[#]] with h （μ） 〈 h＊ （μ） for some point ζ∈D, then there exist infinitely many geodesic segments joining [[0]] and [[μ]], and infinitely many holomorphic geodesic disks containing [[0]] and [μ]] in AT（D）.
ISSN:1439-8516
1439-7617