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Growth theorem of convex mappings on bounded convex circular domains

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Science China Mathematics 1998年第2期41卷 123-130页

作者：刘太顺任广斌 1. Department of Mathematics University of Science and Technology of China 230026 Hefei China

The growth theorem and the 1/2 covering theorem are obtained for the class of normalized biholomorphic convex mappings on bounded convex circular domains, which extend the corresponding results of Sufridge, Thomas, Liu, Gong, Yu, and Wang. The approach is new, which does not appeal to the automorphisms of the domains; and the domains discussed are rather general on which convex mappings can be studied, since the domain may not have a convex mapping if it is not convex.

关键词： convex mappings growth and covering theorem convex circular domains.

Generating Functions for Volume-preserving mappings and Hamilton-Jacobi Equations for Source-free Dynamical Systems

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Science China Mathematics 1994年第10期37卷 1172-1188页

作者：尚在久 Institute of Mathematics Academia Sinica Beijing 100080 PRC

The general generating function theory for volume-preserving mappings and Hamilton-Jacobi theory for source-free systems are developed.

关键词： volume-preserving mappings generating functions source-free systems Hamilton-Jacobi equations.

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 *** is proved that the first (k+1 ) terms ofthe expansions of the jth component fj of such a map / depend only on zj ... 详细信息

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

SUBCLASSES OF BIHOLOMORPHIC mappings UNDER THE EXTENSION OPERATORS

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Acta Mathematica Scientia 2019年第1期39卷 297-311页

作者： Chaojun WANG Yanyan CUI Hao LIU College of Mathematics and Statistics Zhoukou Normal University College of Mathematics and Information Science Hebei Normal University Institute of Contemporary Mathematics Henan University

In this article, we mainly study the invariance of some biholomorphic mappings with special geometric characteristics under the extension operators. First we generalize the Roper-Suffridge extension operators on Bergman-Hartogs domains. Then, by the geometric characteristics of subclasses of biholomorphic mappings, we conclude that the modified Roper-Suff ridge operators preserve the properties of S_Ω~*(β,A, B), parabolic and spirallike mappings of type β and order p, strong and almost spirallike mappings of type 0 and orderα as well as almost starlike mappings of complex order λ on Ω_(p1,…,ps,q)^(B^n) under different conditions, respectively. The conclusions provide new approaches to construct these biholomorphic mappings in several complex variables.

关键词： spirallike mappings Roper-Suffridge operator Bergman-Hartogs domains

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： Yanyan CUI Hao LIU 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

A note on uniqueness problem for meromorphic mappings with 2N+3 hyperplanes

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Science China Mathematics 2010年第10期53卷 2657-2663页

作者： ZhiHua Chen QiMing Yan Tongji Univ Dept Math Shanghai 200092 Peoples R China

In this paper,a uniqueness theorem for meromorphic mappings partially sharing 2N+3 hyperplanes is *** a meromorphic mapping f and a hyperplane H,set E(H,f) = {z|ν(f,H)(z) > 0}.Let f and g be two linearly non-degenerate meromorphic mappings and {Hj}j2=N1+ 3be 2N + 3 hyperplanes in general position such that dim f-1(Hi) ∩ f-1(Hj) n-2 for i = *** that E(Hj,f) E(Hj,g) for each j with 1 j 2N +3 and f = g on j2=N1+ 3f-1(Hj).If liminfr→+∞ 2j=N1+ 3N(1f,Hj)(r) j2=N1+ 3N(1g,Hj)(r) > NN+1,then f ≡ g.

关键词： value distribution theory uniqueness theorem meromorphic mappings

A note on extremal quasi-conformal mappings

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Science China Mathematics 2010年第1期53卷 63-70页

作者： LI ZhongSchool of Mathematical Sciences,Peking University,Beijing 100871,China 1. School of Mathematical Sciences Peking University Beijing 100871 China

An extremal quasi-conformal mapping f of a domain D is said to be of non-landslide type if the set Ef(δ):= {z∈D:|μf(z)|≤||μ|| ∞ -δ} has no interior points for any δ > 0. In this paper,we construct a quasi-conformal mapping f of the unit disc D such that its Teichmu¨ller equivalence class [f] contains infinitely many extremal mappings of non-landslide type. The relation between extremal mappings of non-landslide type and locally extremal mappings is also discussed.

关键词： quasi-conformal mappings extremal quasi-conformal mappings locally extremal quasi-conformal mappings

Bloch Constant of Holomorphic mappings on Bounded Symmetric Domains

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Science China Mathematics 1993年第3期36卷 285-299页

作者：严志敏龚升 Department of Mathematics University of CaliforniaBerkeley California 94720USA Department of Mathematics University of Science and Technology of ChinaHefei 230026PRC

The estimation of the lower bound of the Bloch constant of holomorpbicmappings on irreducible bounded symmetric domains is given.

关键词： bounded symmetric domains Bloch mappings Bloch constant

L-FUZZY PERFECT mappings

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Chinese Science Bulletin 1990年第13期35卷 1067-1071页

作者：徐晓泉 Department of Mathematics Sichuan University Chengdu 610064 PRC Department of Basic CoursesJiangxi Industrial UniversityNanchang 330029.PRC.

Perfect mapping is one of the important notions in topology. It is a noticeable topic to define a proper concept of L-fuzzy perfect mappings. Azad and Chen Bisheng introduced the concepts of fuzzy mappings for the cas... 详细信息

关键词： L-fuzzy perfect mappings invariants inverse invariants.