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extremal problems on the Hua domain of the first type

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Science China Mathematics 2005年第Z1期48卷 343-354页

作者： SU Jianbing & YIN Weiping Mathematics Department, Xuzhou Normal University, Xuzhou 221116, China Mathematics Department, Capital Normal University, Beijing 100037, China Mathematics Department Xuzhou Normal University Xuzhou China Mathematics Department Capital Normal University Beijing China

In this paper we study some extremal problems between the Hua domain of the first type and the unit ball.

关键词： extremal problem, Hua domain of the first type, minimal circumscribed Hermitian ellipsoid.

extremal eigenvalues of measure differential equations with fixed variation

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Science China Mathematics 2010年第10期53卷 2573-2588页

作者： ZHANG MeiRong 1,2 1 Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China 2 Zhou Pei-Yuan Center for Applied Mathematics,Tsinghua University,Beijing 100084,China Department of Mathematical Sciences Tsinghua University Beijing China Zhou Pei-Yuan Center for Applied Mathematics Tsinghua University Beijing China

In this paper we will study eigenvalues of measure differential equations which are motivated by physical problems when physical quantities are not absolutely continuous.By taking Neumann eigenvalues of measure differential equations as an example,we will show how the extremal problems can be completely solved by exploiting the continuity results of eigenvalues in weak* topology of measures and the Lagrange multiplier rule for nonsmooth functionals.These results can give another explanation for extremal eigenvalues of SturmLiouville operators with integrable potentials.

关键词： measure differential equation eigenvalue extremal value weak* topology Frechét derivative sub-differential

extremal polygonal quasiconformal mappings and biLipschitz mappings

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Science China Mathematics 2010年第5期53卷 238-245页

作者： Huang HuaYing Wu ShengJian Peking Univ Sch Math Sci LMAM Beijing 100871 Peoples R China

We show that the extremal polygonal quasiconformal mappings are biLipschitz with respect to the hyperbolic metric in the unit disk.

关键词： quasiconformal mapping extremal polygonal quasiconformal mapping hyperbolic metric

A remark on "an approximation condition and extremal quasiconformal extension

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Chinese Science Bulletin 1997年第21期42卷 1765-1767页

作者： Chen, JX Chen, ZG Fudan Univ Dept Math Shanghai 200433 Peoples R China

LET D be the unit disk in the complex plane C and f be a sense preserving quasisymmetrichomeomorphism of D onto itself. Denote by Q a quadrilateral D （z1, z2, z3, z4 ） with do-main D and vertices z1, z2, z3, z4 ∈D,... 详细信息

关键词： quasisymmetric function extremal quasiconformal mapping Teichmüller mapping.

A problem in extremal quasiconformal extensions

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Science China Mathematics 1998年第11期41卷 1135-1141页

作者：漆毅 School of Mathematical Sciences Peking University Beijing China

A constant K (m) 0(h) is introduced for every quasisymmetric mapping h of the unit circle and every integer m ≥4 which contains the constant K 0(h) (indicated by the change in module of the quadrilaterals with vertices on the circle) as a special case. A necessary and sufficient condition is established for K (m) 0(h)=K 1(h) . It is shown that there are infinitely many quasisymmetric mappings of the unit circle having the property that K (m) 0(h)

关键词： quasisymmetric mappings Teichmüller spaces extremal mapping.

Minimal circumscribed Hermitian ellipsoid of Hartogs domains and an application to an extremal problem

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Science China Mathematics 2009年第8期52卷 1699-1716页

作者： AHN Heung-ju PARK Jong-do Department of Mathematical Sciences Seoul National University School of Mathematics Korea Institute for Advanced Study Hoegiro 87 Dongdaemun-gu Seoul 130-722 Korea

In this paper we construct circumscribed Hermitian ellipsoids of Hartogs domains of least volume and as an application, we obtain the Carath′eodory extremal mappings between the Hartogs domains and the unit ball, and... 详细信息

关键词： Hartogs domain minimal circumscribed Hermitian ellipsoid extremal problem

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

CHARACTERIZATION OF PRIMITIVE extremal MATRICES

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Science China Mathematics 1991年第7期34卷 791-802页

作者：柳柏濂邵嘉裕 South China Normal University Guangzhou 510631 PRC Tongji University Shanghai 200092 PRC

Let D（n,d）={A|A is an n×n primitive matrix with d positive diagonal elements}. Itis well known that γ（A）≤2n-d-1 for A∈D（n,d）. Suppose D1（n,d）={A∈D（n,d） |γ（A）=2n-d-1} is the set of extremal matrices i... 详细信息

关键词： primitive extremal matrix characterization exponent.

On the extremal sets of extremal quasiconformal mappings

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Science China Mathematics 2003年第4期46卷 552-561页

作者：周泽民陈纪修杨宗信 School of Mathematics Peking UniversityBeijing 100871China Department of Mathematics Fudan UniversityShanghai 200433China Institute of Matnematics Fudan UniversityShanghai 200433China

The properties of the extremal sets of extremal quasiconformal mappings are discussed. It is proved that if an extremal Beltrami coefficientμ(z) is not uniquely extremal, then there exists an extremal Beltrami coefficient v(z) in its equivalent class and a compact subset E ( ) △ with positive measure such that the essential upper bound of ν(z) on E is less than the norm of [μ].

关键词： extremal quasiconformal mapping, uniquely extremal quasiconformal mapping, extremal set, admissible variation.