Asymptotic Teichmüller space. II. The metric structure

Earle, Clifford J.; Gardiner, Frederick P.; Lakic, Nikola

doi:10.1090/conm/355/06452

Cited by 45 publications

(53 citation statements)

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“…It is known that for every Fuchsian group Γ, the Teichmüller distance on T (Γ) coincides with the Kobayashi distance, which is proved by Gardiner [10]. Earle, Gardiner and Lakic [8] proved that the Teichmüller distance coincides with the Kobayashi distance on the metric subspace of all Teichmüller equivalence classes represented by asymptotically conformal maps. Hu, Jiang and Wang [13] showed this result more directly in T (1).…”

Section: Introductionmentioning

confidence: 94%

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Introduction of a complex structure on the p-integrable Teichmüller space

Yanagishita

2014

Ann. Acad. Sci. Fenn. Math.

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Abstract. For p ≥ 1, the p-integrable Teichmüller space is the metric subspace of the Teichmüller space composed of the Teichmüller equivalence classes with p-integrable Beltrami coefficient. In this paper, for p ≥ 2, we introduce a complex structure on the p-integrable Teichmüller space of an arbitrary Fuchsian group satisfying a certain geometric condition. As an application, we show the coincidence of two canonical distances on the metric subspace.

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Section: Introductionmentioning

confidence: 94%

“…It is known that the Teichmüller distance on T 0 (Γ) coincides with the Kobayashi distance (cf. [8]). …”

Section: Masahiro Yanagishitamentioning

confidence: 99%

Introduction of a complex structure on the p-integrable Teichmüller space

Yanagishita

2014

Ann. Acad. Sci. Fenn. Math.

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“…], which is also isometric with respect to d A ; see [6]. Let Aut(AT (R)) be the group of all biholomorphic automorphisms of AT (R).…”

Section: Mod(r) = ι(Mcg(r))mentioning

confidence: 99%

Pure mapping class group acting on Teichmüller space

Fujikawa

2008

Conform. Geom. Dyn.

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Abstract. For a Riemann surface of analytically infinite type, the action of the quasiconformal mapping class group on the Teichmüller space is not discontinuous in general. In this paper, we consider pure mapping classes that fix all topological ends of a Riemann surface and prove that the pure mapping class group acts on the Teichmüller space discontinuously under a certain geometric condition of a Riemann surface. We also consider the action of the quasiconformal mapping class group on the asymptotic Teichmüller space. Non-trivial mapping classes can act on the asymptotic Teichmüller space trivially. We prove that all such mapping classes are contained in the pure mapping class group.

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“…[5], [6] and [7]). In their works, the proposition was obtained as a consequence of general principles for holomorphic mappings on domains in Banach spaces.…”

Section: Proposition 41 (Allowable Bijections) Let R and S Be Riemamentioning

confidence: 99%

“…Invariant distances are powerful tools for studying the analytic structures of complex Banach manifolds (cf. [3] and [9]) and are also important objects of research in Teichmüller theory (see [6] and [10]). The Carathéodory distance and the Kobayashi distance are typical examples of invariant distances.…”

Section: Introductionmentioning

confidence: 99%