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asymptotic teichmüller space

Proceedings of the Edinburgh Mathematical Society (1)

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On Geodesics in Asymptotic Universal Teichmüller Space
Part of
- Complex dynamical systems
Zhou Zemin, Chen Jixiu
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 59 / Issue 4 / November 2016

Published online by Cambridge University Press:

08 January 2016, pp. 1065-1074
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Let AT(Δ) be the asymptotic universal Teichmüller space, viewed as the space of all asymptotic Teichmüller equivalence classes [[μ]]. We show that if μ is asymptotically extremal in AT(Δ) and hp([[μ]]) < h([[μ]]) for some boundary point p of Δ, then there are infinitely many geodesics joining [[0]] and [[μ]] in AT(Δ). As a corollary, a necessary condition for a complex dilatation to be uniquely extremal in AT(Δ) is given.