Some characterizations of the integrable Teichmüller space

Tang, Shuan

doi:10.1007/s11425-012-4472-1

Cited by 24 publications

(13 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then there exists ν ∈ τ −1 such that ν belongs to Ael p (Γ τ ). It follows from the proof of Theorem 2.1 in [20] that…”

Section: Characterization Of T P (γ) By Douady-earle Extensionsmentioning

confidence: 95%

“…Specifically, we characterize each point of T p (Γ) by its Douady-Earle extension, which is a quasiconformal self-mapping on ∆ with conformal naturality (see [6]). Originally, Cui [5] proved this result in the case of T 2 (1) and Tang [20] extended it to T p (1) for p ≥ 2, where 1 = {id ∆ } is the trivial group. In the proof, they applied the Dirichlet integral of harmonic self-maps on ∆ obtained by the Poisson integral (see [4]).…”

Section: Introductionmentioning

confidence: 90%

See 1 more Smart Citation

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

Yanagishita

2014

Ann. Acad. Sci. Fenn. Math.

View full text Add to dashboard Cite

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.

show abstract

“…Then there exists ν ∈ τ −1 such that ν belongs to Ael p (Γ τ ). It follows from the proof of Theorem 2.1 in [20] that…”

Section: Characterization Of T P (γ) By Douady-earle Extensionsmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 90%

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

Yanagishita

2014

Ann. Acad. Sci. Fenn. Math.

View full text Add to dashboard Cite

show abstract

“…where ρ D (z) = 2/(1 − |z| 2 ) is the hyperbolic density on D. The space of all p-integrable Beltrami coefficients on D is denoted by Ael p (D). The p-integrable Teichmülcer spaces defined below have been studied by Cui [5], Guo [13], Shen [25], Takhtajan and Teo [26], Tang [27] and Yanagishita [28] among others.…”

Section: The P-integrable Teichmüller Spacementioning

confidence: 99%

Injectivity of the quotient Bers embedding of Teichmüller spaces

Matsuzaki¹

2019

Ann. Acad. Sci. Fenn. Math.

View full text Add to dashboard Cite

The Bers embedding of the Teichmüller space is a homeomorphism into the Banach space of certain holomorphic automorphic forms. For a subspace of the universal Teichmüller space and its corresponding Banach subspace, we consider whether the Bers embedding can project down between their quotient spaces. If this is the case, it is called the quotient Bers embedding. Injectivity of the quotient Bers embedding is the main problem in this paper. Alternatively, we can describe this situation as the universal Teichmüller space having an affine foliated structure induced by this subspace. We give several examples of subspaces for which the injectivity holds true, including the Teichmüller space of circle diffeomorphisms with Hölder continuous derivative. As an application, the regularity of conjugation between representations of a Fuchsian group into the group of circle diffeomorphisms is investigated.2010 Mathematics Subject Classification. Primary 30F60, Secondary 37E30.

show abstract

“…Radnell, Schippers and Staubach [47,48,50,51] did this for bordered surfaces of type (g, n). M. Yanagishita [79] extended the L p theory of Guo [22] and Tang [75] to surfaces satisfying "Lehner's condition", which includes bordered surfaces of type (g, n). In the L 2 -setting the two Teichmüller spaces are the same as sets, but the constructions of the complex structures are rather different.…”

Section: 3mentioning

confidence: 99%

Comparison Moduli Spaces of Riemann Surfaces

Schippers

Staubach

2017

Trends in Mathematics

View full text Add to dashboard Cite

We define a kind of moduli space of nested surfaces and mappings, which we call a comparison moduli space. We review examples of such spaces in geometric function theory and modern Teichmüller theory, and illustrate how a wide range of phenomena in complex analysis are captured by this notion of moduli space. The paper includes a list of open problems in classical and modern function theory and Teichmüller theory ranging from general theoretical questions to specific technical problems.

show abstract

Some characterizations of the integrable Teichmüller space

Cited by 24 publications

References 9 publications

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

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

Injectivity of the quotient Bers embedding of Teichmüller spaces

Comparison Moduli Spaces of Riemann Surfaces

Contact Info

Product

Resources

About