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Homogeneous expansions of normalized biholomorphic convex mappings over B^p

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Science China Mathematics 1997年第8期40卷 799-806页

作者：刘太顺张文俊 Department of Mathematics University of Science and Technology of ChinaHefei 230026China Department of Mathematics Shenzhen UniversityShenzhen 518060China

The power series expansions of normalized biholomorphic convex mappings on the Reinhardt domain are studied.It is proved that the first (k+1 ) terms ofthe expansions of the jth component fj of such a map / depend only... 详细信息

关键词： biholomorphic convex mappings Reinhardt domains Schwarz-type lemma.

THE INVARIANCE OF SUBCLASSES OF biholomorphic MAPPINGS ON BERGMAN-HARTOGS DOMAINS

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Acta Mathematica Scientia 2019年第4期39卷 1103-1120页

作者：崔艳艳刘浩 College of Mathematics and Statistics Zhoukou Normal University Zhoukou 466001 China Institute of Contemporary Mathematics Henan University Kaifeng 475007 China

We mainly discuss the invariance of some subclasses of biholomorphic mappings under the generalized Roper-Suffridge operators on Bergman-Hartogs domains which are based on the unit ball Bn. Using the geometric properties and the distortion results of subclasses of biholomorphic mappings, we obtain the geometric characters of almost spirallike mappings of type β and order α, S_?~*(β, A, B), strong and almost spirallike mappings of type βand order α maintained under the generalized Roper-Suffridge operators on Bergman-Hartogs domains. Sequentially, we conclude that the generalized operators and the known operators preserve the same properties under some conditions. The conclusions generalize some known results.

关键词： biholomorphic mappings spirallike mappings Bergman-Hartogs domain Roper-Suffridge operator

On Decomposition Theorem of normalized biholomorphic convex mappings in Reinhardt domains

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Science China Mathematics 2003年第1期46卷 94-106页

作者：张文俊刘太顺 Department of Mathematics Shenzhen University Normal College Department of Mathematics University of Science and Technology of China

The construction of normalized biholomorphic convex mappings in the Reinhardt domain Dp{(z1,z2,....zn):z1 p1+z1 p2+....+zn pn 2,j=1,2,.....n,) of n is discussed.The authors set up a Decomposition Theorem for such mappings. As a special case, it is proved that, for each suchthis derives the Decomposition Theorem of normalized biholo morphic convex mappings in the polydisc whichwas gotten by T.J. Suffridge in 1970.

关键词： Reinhardt domain, biholomorphic convex mapping, Schwarz Lemma, Decomposition Theorem.

A NECESSARY AND SUFFICIENT CONDITION:biholomorphic MAPPINGS ARE STARLIKE ON A CLASS OF REINHARDT DOMAINS

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Chinese Science Bulletin 1991年第14期36卷 1151-1153页

作者：龚昇王世坤余其煌 University of Science and Technology of China Hefei 230026 PRC Institute of Applied Mathematics Academia Sinica Beijing 100080 PRC

1. In [1], T. J. Suffridge gave the necessary and sufficient condition for local biholomorphic mappings on the Reinhardt domains , to be starlike. Using this condition Yu Qihuang et al. gave the growth theorem and covering theorem for normalized biholomorphic starlike mappings in D_p. In this note we give a necessary and suffident condition for local biholomorphic mappings on more general Reinhardt

关键词： biholomorphic mapping starlike mapping Reinhardt domains.

Projection on Segre varieties and determination of holomorphic mappings between real submanifolds Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

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Science China Mathematics 2006年第11期49卷 1611-1624页

作者： BAOUENDI M S EBENFELT Peter ROTHSCHILD Linda P Department of Mathematics University of California at San Diego La JollaCA 92093-0112USA

It is shown that a germ of a holomorphic mapping sending a real-analytic generic submanifold of finite type into another is determined by its projection on the Segre variety of the target manifold. A necessary and sufficient condition is given for a germ of a mapping into the Segre variety of the target manifold to be the projection of a holomorphic mapping sending the source manifold into the target. An application to the biholomorphic equivalence problem is also given.

关键词： Segre variety, generic submanifold, Segre mappings, finite type, biholomorphic equivalence.

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 Teichmüller spaces, including the Bers fiber space and Teichmüller curve, establishing an isomorphism theorem between "punctured" Teichmüller curves... 详细信息

关键词： Teichmüller space, Bers fiber space, "punctured" fiber space, Teichmüller curve, "punctured" Teichmüller 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 Γ such that H/Γ is a hyperbolic Riemann surface, the Teichmüller curve V(Γ) has a unique complex manifold structure so that the natural projection of the Bers fiber space F(Γ) onto V(Γ) is holomorphic with local holomorphic sections.An isomorphism theorem for Teichmüller curves is deduced, which generalizes a classical result that the Teichmüller curve V(Γ) depends only on the type of Γ and not on the orders of the elliptic elements of Γ when H/Γ is a compact hyperbolic Riemann surface.

关键词： Teichmüller space, Bers fiber space, Teichmüller curve, biholomorphic isomorphism.

Homeomorphic extension of strongly spirallike mappings in C^n

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Science China Mathematics 2010年第1期53卷 87-100页

作者： CURT Paula KOHR Gabriela KOHR Mirela Faculty of Economics and Business Administration Babes-Bolyai University 58-60 Teodor Mihali Str.400591 Cluj-NapocaRomania Faculty of Mathematics and Computer Science Babes-Bolyai University1 M.Kogaǎlniceanu Str.400084 Cluj-NapocaRomania

In this paper we consider a proper subclass nA of the full class of spirallike mappings on the Euclidean unit ball Bn in Cn with respect to a given linear operator A. We use the method of subordination chains to obtain an upper growth result for nA , and we obtain various examples of mappings in the same class of normalized biholomorphic mappings on the unit ball Bn in Cn . We also prove that the class nA is compact, while the full class of spirallike mappings with respect to a linear operator need not be compact in dimension n≥2, even when the operator is diagonal. This is one of the motivations for considering the class nA . Finally we prove that if f is a quasiregular strongly spirallike mapping on Bn such that ||[Df(z)]-1 Af(z)|| is uniformly bounded on Bn , then f extends to a homeomorphism of R2n onto itself. In addition, if A + A* = 2aI n for some a >0, this extension is also quasiconformal on R2n .

关键词： biholomorphic mapping quasiregular mapping quasiconformal mapping spirallikeness strongly spirallikeness subordination subordination chain

Convex mappings on some circular domains

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Science China Mathematics 2010年第5期53卷 228-237页

作者： Hong Yi Chen WenGe S China Univ Technol Dept Math Guangzhou 510640 Guangdong Peoples R China

In this paper,we consider some circular domains.And we give an extension theorem for some normalized biholomorphic convex mapping on some circular domains.Especially,we discover the normalized biholomorphic convex mapping on some circular domains have the form f(z) =(f1(z1),...,fn(zn)),where fj:D → C are normalized biholomorphic convex mapping.

关键词： circular domain biholomorphic convex mapping Minkowski functional Schwarz lemma