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国家自然科学基金(10826083)

作品数:6 被引量:4H指数:1
相关作者:王建飞徐辉明刘太顺更多>>
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Distortion theorems on the Lie ball R_(IV)(n) in C^n
2009年
In this paper,we introduce the subfamilies Hm(RIV(n))of holomorphic mappings defined on the Lie ball RIV(n)which reduce to the family of holomorphic mappings and the family of locally biholomorphic mappings when m=1 and m→+∞,respectively.Various distortion theorems for holomophic mappings Hm(RIV(n))are established.The distortion theorems coincide with Liu and Minda’s as the special case of the unit disk.When m=1 and m→+∞,the distortion theorems reduce to the results obtained by Gong for RIV(n),respectively.Moreover,our method is different.As an application,the bounds for Bloch constants of Hm(RIV(n))are given.
WANG JianFei1,LIU TaiShun2 &XU HuiMing1 1College of Mathematics,Physics and Information Engineering,Zhejiang Normal University,Jinhua 321004, China 2D epartment of Mathematics,Huzhou Teachers College,Huzhou 313000,China
关键词:HOLOMORPHICMAPPINGTHEOREMBLOCHBLOCHMAPPING
DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC D^n被引量:1
2010年
In this article, we establish distortion theorems for some various subfamilies of Bloch mappings defined in the unit polydisc Dn with critical points, which extend the results of Liu and Minda to higher dimensions. We obtain lower bounds of | det(f'(z))|and Rdet(f'(z)) for Bloch mapping f. As an application, some lower and upper bounds of Bloch constants for the subfamilies of holomorphic mappings are given.
王建飞刘太顺唐笑敏
A Simple Proof of the Lower Bounds of Distortion Theorems on the Roper-Suffridge Operator
2009年
Liczberski-Starkov firstfound a lower bound for ||D(f)|| near the origin, where f(z)=(F(z1),√F1(z1)z2,…,√F'(z1)zn)'is the Roper-Suffridge operator on the unit ball Bn in Cn and F is a normalized convex function on the unit disk. Later, Liczberski-Starkov and Hamada-Kohr proved the lower bound holds on the whole unit ball using a complex computation. Here we provide a rather short and easy proof for the lower bound. Similarly, when F is a normalized starlike function on the unit disk, a lower bound of ||D(f)|| is obtained again.
WANG Jian-feiLIU Tai-shun
Distortion Theorem for Bloch Mappings on the Unit Ball ■~n被引量:1
2009年
In this paper, we obtain a version of subordination lemma for hyperbolic disk relative to hyperbolic geometry on the unit disk D. This subordination lemma yields the distortion theorem for Bloch mappings f ∈ H(B^n) satisfying ||f||0 = 1 and det f'(0) = α ∈ (0, 1], where||f||0 = sup{(1 - |z|^2 )n+1/2n det(f'(z))[1/n : z ∈ B^n}. Here we establish the distortion theorem from a unified perspective and generalize some known results. This distortion theorem enables us to obtain a lower bound for the radius of the largest univalent ball in the image of f centered at f(0). When a = 1, the lower bound reduces to that of Bloch constant found by Liu. When n = 1, our distortion theorem coincides with that of Bonk, Minda and Yanagihara.
Jian Fei WANGTai Shun LIU
关键词:HOLOMORPHIC
The Distortion Theorems for k-fold Symmetric Quasi-convex Mappings along a Unit Direction in C^n被引量:1
2012年
We obtain a distortion theorem of Jacobian matrix Jf(z) for k-fold symmetric quasi-convex f along a unit direction in C^n on the unit polydisc.
卢金刘太顺王建飞
C^n中Lie球R_(Ⅳ)(n)上的偏差定理被引量:1
2009年
本文引入了Lie球双曲空间上映照族Hm(RIV(n)),满足m阶Jacobi行列式为零的全纯映照子族.而且当m趋于无穷时,该映照族就是RIV(n)上的局部双全纯映照族.作者用分析的方法给出了Hm(RIV(n))上的偏差定理.当m=1和m→+∞时,结果分别都回到了Gong关于Lie球RIV(n)上的偏差定理;当n=1,其结果又回到了Liu和Minda在单位圆盘上的偏差定理.本文的方法也不同于以前.作为偏差定理的一个应用,给出了不同映照族Hm(RIV(n))上的Bloch常数估计.
王建飞刘太顺徐辉明
关键词:全纯映照偏差定理BLOCH常数
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