Holomorphic contractibility and other properties of the Weil-Petersson and VMOA Teichmüller spaces

Fan, Jishan; Hu, Jun

doi:10.5186/aasfm.2016.4137

Cited by 15 publications

(5 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It was shown by Fan and Hu [12] that the Kobayashi distance d K defined on the complex manifold T v coincides with the restriction of the Teichmüller distance d T . In fact, d K = d i T = d T on T v .…”

Section: Properties Of the Carleson Distancementioning

confidence: 95%

BMO Teichmüller spaces and their quotients with complex and metric structures

Wei,

Matsuzaki

2018

Preprint

View full text Add to dashboard Cite

The paper presents some recent results on the BMO Teichmüller space, its subspaces and quotient spaces. We first consider the chord-arc curve subspace and prove that every element of the BMO Teichmüller space is represented by its finite composition. Moreover, we show that these BMO Teichmüller spaces have affine foliated structures induced by the VMO Teichmüller space. By which, their quotient spaces have natural complex structures modeled on the quotient Banach space. Then, a complete translation-invariant metric is introduced on the BMO Teichmüller space and is shown to be a continuous Finsler metric in a special case.

show abstract

Section: Properties Of the Carleson Distancementioning

confidence: 95%

BMO Teichmüller spaces and their quotients with complex and metric structures

Wei,

Matsuzaki

2018

Preprint

View full text Add to dashboard Cite

show abstract

“…The holomorphic contractibility of T 2 , which means that the contraction φ(•, t) is holomorphic for each fixed t ∈ [0, 1], was obtained by Fan and Hu [9] though this does not imply the existence of a global holomorphic section for π .…”

Section: Corollary 14 Under the Identification Of W P (R) With T P T...mentioning

confidence: 99%

The p-Weil–Petersson Teichmüller Space and the Quasiconformal Extension of Curves

Wei

Matsuzaki

2022

J Geom Anal

View full text Add to dashboard Cite

We consider the correspondence between the space of p-Weil–Petersson curves $$\gamma $$ γ on the plane and the p-Besov space of $$u=\log \gamma '$$ u = log γ ′ on the real line for $$p > 1$$ p > 1 . We prove that the variant of the Beurling–Ahlfors extension defined by using the heat kernel yields a holomorphic map for u on a domain of the p-Besov space to the space of p-integrable Beltrami coefficients. This in particular gives a global real-analytic section for the Teichmüller projection from the space of p-integrable Beltrami coefficients to the p-Weil–Petersson Teichmüller space.

show abstract

“…Fan and Hu [11] proved that the image domain of T v under the Bers embedding is holomorphically contractible in the sense that there is a contraction : T v × [0, 1] → T v such that is continuous and (•, t) is holomorphic for each fixed t.…”

Section: And Is a Real-analytic Mapping Alternatively Another Real-an...mentioning

confidence: 99%

“…Then, with respect to the complex structure of SS C (S) given as above, we see the following: ). For μ 1 ∈ M 0 (D), the same notation μ 1 denotes the Beltrami coefficient on D * given by the reflection (11), and similarly for μ 2 ∈ M 0 (D * ), μ 2 ∈ M 0 (D) denotes its reflection. Let j be the anti-holomorphic involution of SS C (S) defined by…”

Section: Real-analytic Mapping To the Space Of Vmo [Theorem 11 (I)]mentioning

confidence: 99%

The VMO-Teichmüller space and the variant of Beurling–Ahlfors extension by heat kernel

Wei

Matsuzaki

2022

Math. Z.

View full text Add to dashboard Cite

We give a real-analytic section for the Teichmüller projection onto the VMO-Teichmüller space by using the variant of Beurling–Ahlfors extension by heat kernel introduced by Fefferman et al. (Ann Math 134:65–124, 1991). Based on this result, we prove that the VMO-Teichmüller space can be endowed with a real Banach manifold structure that is real-analytically equivalent to its complex Banach manifold structure. We also obtain that the VMO-Teichmüller space admits a real-analytic contraction mapping.

show abstract

Holomorphic contractibility and other properties of the Weil-Petersson and VMOA Teichmüller spaces

Cited by 15 publications

References 25 publications

BMO Teichmüller spaces and their quotients with complex and metric structures

BMO Teichmüller spaces and their quotients with complex and metric structures

The p-Weil–Petersson Teichmüller Space and the Quasiconformal Extension of Curves

The VMO-Teichmüller space and the variant of Beurling–Ahlfors extension by heat kernel

Contact Info

Product

Resources

About