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...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.展开更多
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）...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.展开更多
The estimations of the bounds of the Bloch constant of locally biholomorphic mappingson irreducible bounded symmetric domains are given. When the domain is a unit circle, theestimation of the lower bounds is just the ...The estimations of the bounds of the Bloch constant of locally biholomorphic mappingson irreducible bounded symmetric domains are given. When the domain is a unit circle, theestimation of the lower bounds is just the famous one-half estimation.展开更多
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 a...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.展开更多
基金partly supported by the National Natural Science Foundation of China(10826083,10971063)NSF of Zhejiang Province (D7080080, Y606197,Y6090694)Scientific Research Fund of Zhejiang Provincial Education Department (Y200805520)
文摘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.
基金supported by NNSF of China (Grant No.10826083)supported by NNSF of China (Grant No.10571164)+1 种基金NSF of Zhejiang province (Grant No.D7080080)SRFDP of Higher Education (Grant No.20050358052)
文摘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.
文摘The estimations of the bounds of the Bloch constant of locally biholomorphic mappingson irreducible bounded symmetric domains are given. When the domain is a unit circle, theestimation of the lower bounds is just the famous one-half estimation.
基金supported by National Natural Science Foundation of China(Grant No.10826083,10771064)Specialized Research Fund for the Doctoral Program of Higher Education(SRFDP)(Grant No.20050358052)Natural Science Foundation of Zhejiang Province(Grant No.D7080080,Y6090694)
文摘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.
