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A Brief Approach to a Riemann-Hilbert Problem on Quasi-circles

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Chinese Annals of Mathematics,Series B 2024年第6期45卷 971-978页

作者： Tailiang LIU yuliang shen Department of Mathematics Soochow University

Abstract The authors introduce the Sobolev space ■on a quasi-circleΓand give a fast approach to the jump formula which gives a decomposition of an element in ■as the boundary values of two Dirichlet functions in th... 详细信息

关键词： 30C62 Dirichlet space Quasi-circle Quasiconformal mapping Sobolev space

On the Compactness of Grunsky Differential Operators

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Chinese Annals of Mathematics,Series B 2020年第4期41卷 559-572页

作者： Li WU yuliang shen Department of Mathematics Soochow UniversitySuzhou 215006JiangsuChina.

Grunsky operators play an important role in classical geometric function theory and in the study of Teichmüller *** Grunsky map is known to be holomorphic on the universal Teichmüller *** this paper the authors deal with the compactness of a Grunsky differential *** will give upper and lower estimates of the essential norm of a Grunsky differential operator and discuss when a Grunsky differential operator is a p-Schatten class operator.

关键词： Universal Teichmüller space Beltrami coefficient Grunsky operator Compact operator p-Schatten class operator Essential norm

Fourier coefficients of Zygmund functions and analytic functions with quasiconformal deformation extensions

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Science China Mathematics 2012年第3期55卷 607-624页

作者： shen yuliang Department of Mathematics Soochow University Suzhou 215006 China

An open problem is to characterize the Fourier coefficients of Zygmund *** problem was also explicitly suggested by Nag and later by Teo and Takhtajan-Teo in the course of study of the universal Teichmu¨ller *** a complex analysis approach,we give a characterization for the Fourier coefficients of a Zygmund function by a quadratic *** related topics are also discussed,including those analytic functions with quasiconformal deformation extensions.

关键词： Zygmund function Fourier coefficient quasiconformal deformation analytic function

Isomorphisms of fiber spaces over Teichmüller spaces

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Science China Mathematics 2006年第7期49卷 877-892页

作者： HU Yun shen yuliang Department of Mathematics Suzhou University Suzhou 215006 China Department of Mathematics Suzhou University Suzhou 215006 China

We will be mainly concerned with some important fiber spaces over Teichmuller spaces, including the Bers fiber space and Teichmuller curve, establishing an isomorphism theorem between 'punctured' Teichmuller curves an... 详细信息

关键词： Teichmuller space Bers fiber space 'punctured' fiber space Teichmuller curve 'punctured' Teichmuller curve biholomorphic isomorphism.

An isomorphism theorem for Teichmüller curves

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Science China Mathematics 2006年第5期49卷 577-586页

作者： CAI Yongmao shen yuliang Department of Mathematics Suzhou University Suzhou 215006China Department of Mathematics Suzhou University Suzhou 215006China

It is proved that for any Fuchsian group Г such that H/Г is a hyperbolic Riemann surface, the Teichmuller curve V(Г) has a unique complex manifold structure so that the natural projection of the Bers fiber space F(Г) onto V(Г) is holomorphic with local holomorphic sections. An isomorphism theorem for Teichmuller curves is deduced, which generalizes a classical result that the Teichmuller curve V(Г) depends only on the type of Г and not on the orders of the elliptic elements of Г when H/Г is a compact hyperbolic Riemann surface.

关键词： Teichmuller space Bers fiber space Teichmuller curve biholomorphic isomorphism.

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On Strebel points

Science China Mathematics 2009年第9期52卷 2019-2026页

作者： HU Yun shen yuliang Department of Mathematics Soochow UniversitySuzhou 215006China

Any Beltrami coefficient μ on a hyperbolic Riemann surface X of infinite type represents a point [μ]T in the Teichmüller space T (X) and a point [μ]B in the tangent space of T (X) at the base point as well. The paper deals with the problem of determining whether that [μ]T is a Strebel point is equivalent to that [μ]B is an infinitesimal Strebel point.

关键词： Teichmüller space Strebel point infinitesimal Strebel point 32G15 30C62 30F60

Besov Functions and Tangent Space to the Integrable Teichmüller Space

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Chinese Annals of Mathematics,Series B 2018年第6期39卷 963-972页

作者： Shu'an TANG Xiaogao FENG yuliang shen Department of Mathematics Soochow UniversitySuzhou 215006JiangsuChina Department of Mathematics Guizhou Normal UniversityGuiyang 550001China College of Mathmatics and Information China West Normal UniversityNanchong 637002SichuanChina

The authors identify the function space which is the tangent space to the integrable Teichmfiller space. By means of quasiconformal deformation and an operator induced by a Zygmund function, several characterizations ... 详细信息

关键词： Universal Teichmuller space Integrable Teichmuller space Zygmund function Quasiconformal deformation Besov function

Zygmund functions on the real line and quasiconformal deformations

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Science China Mathematics 2013年第4期56卷 757-769页

作者： shen yuliang LIU HongXia WANG LiJun Department of Mathematics Soochow University

By a complex approach,we obtain some results concerning Zygmund functions on the real line,which corresponds to some classical results about Zygmund functions on the unit circle.

关键词： Zygmund function quasiconformal deformation analytic function

A unified approach to the weighted Grtzsch and Nitsche problems for mappings of finite distortion

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Science China Mathematics 2016年第4期59卷 673-686页

作者： FENG XiaoGao TANG ShuAn WU Chong shen yuliang Department of Mathematics Soochow University College of Mathmatics and Information China West Normal University Department of Mathematics Southwest Jiaotong University

This note deals with the existence and uniqueness of a minimiser of the following Grtzsch-type problem inf f ∈F∫∫_(Q_1)φ(K(z,f))λ(x)dxdyunder some mild conditions,where F denotes the set of all homeomorphims f with finite linear distortion K(z,f)between two rectangles Q_1 and Q_2 taking vertices into vertices,φ is a positive,increasing and convex function,and λ is a positive weight function.A similar problem of Nitsche-type,which concerns the minimiser of some weighted functional for mappings between two annuli,is also *** by-products,our discussion gives a unified approach to some known results in the literature concerning the weighted Grtzsch and Nitsche problems.

关键词： mapping of finite distortion weighted Grtzsch problem weighted Nitsche problem