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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.

SHARP ESTIMATES OF QUASI-CONVEX mappings OF TYPE B AND ORDER α

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Acta Mathematica Scientia 2019年第5期39卷 1265-1276页

作者：刘名生吴芬杨燕 School of Mathematical Sciences South China Normal University Guangzhou 510631 China School of Mathematics(Zhuhai) Sun Yat-Sen University Zhuhai 519080 China

In this paper, we first establish several sharp inequalities of homogeneous expansion for biholomorphic quasi-convex mappings of type B and order α on the unit ball E in a complex Banach space X by applying the method and technique of complex analysis. Then, as the application of these sharp inequalities, we derive the sharp estimate of third homogeneous expansions for the above mappings defined on the unit polydisk U^n in C^n.

关键词： quasi-convex mappings of type B and order α inequalities of homogeneous expansions the sharp estimate of third homogeneous expansions

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

The closed finite-to-one mappings and their applications

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Applied Mathematics(A Journal of Chinese Universities) 2019年第2期34卷 149-161页

作者： YANG Jie LIN Shou School of Mathematics and Statistics Minnan Normal UniversityZhangzhouFujian 363000China Department of Mathematics Ningde Normal UniversityNingdeFujian 352100China

In this paper, we discuss the closed finite-to-one mapping theorems on generalized metric spaces and their applications. It is proved that point-Gδ properties,?0-snf-countability and csf-countability are invariants and inverse invariants under closed finite-to-one mappings. By the relationships between the weak first-countabilities, we obtain the closed finite-to-one mapping theorems of weak quasi-first-countability, quasi-first-countability, snf-countability, gfcountability and sof-countability. Furthermore, these results are applied to the study of symmetric products of topological spaces.

关键词： finite-to-one mappings closed mappings weak first-countability sn-networks cs-networks symmetric products

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：王朝君崔艳艳刘浩 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

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

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 School of Mathematical Sciences Peking University Beijing 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

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 proved.For 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 = j.Assume 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