共查询到20条相似文献,搜索用时 15 毫秒
1.
Yuming Chu Gendi Wang Xiaohui Zhang 《Journal of Mathematical Analysis and Applications》2007,326(2):1328-1333
In this paper, we prove that the inner and outer linearly locally connected sets of Rn are invariant respectively under quasiconformal mappings which fixed the point at infinity. On the other hand, we prove the converses of above results to be true also. 相似文献
2.
作为John域的推广,本文定义了弱John域,并讨论了弱John域与拟圆、弱John域与拟共形 映射之间的关系,得到(1)若(?)。中的Jordan域D和它的外部 均是弱John域,则D 是拟圆;(2)R2中的弱John域是拟共不变的;(3)R2中的有界拟圆必是弱John域.最后构造例子 说明R2中的无界拟圆不一定是弱John域. 相似文献
3.
设D是扩充复平面R-2中的单连通Jordan真子域,D*=R-2\D-是D的外部.本文肯定并证明 了K.Hag在1999年提出的如下两个悬而未决的问题:(1)D是Cigar域当且仅当D是OLC域; (2)D是Turning域当且仅当D*是Cigar域. 相似文献
5.
《复变函数与椭圆型方程》2012,57(11):967-985
We show that a domain R ? ? has the property that ?(𝔻) is a quasidisk for all ? for which ?v′(𝔻) ? R if and only if there is a compact K ? ? such that rK ∩ (?\R) ≠ Ø for all r > 0. This constitutes a refinement of the well-known Noshiro–Warschawski univalence criterion. 相似文献
6.
In this paper we define two classes of quasiconformal mappings,and study their covering properties by methods of module.We obtain some new results.In the meantime,we give new methods to prove Koebe 1/2 covering theorem on convex conformal mappings. 相似文献
7.
In this note we show that a harmonic quasiconformal mapping f=u+iv with respect to the Poincaré metric of the upper half plane onto itself such that v(x,y)=v(y) or u(x,y)=u(x) is a conformal mapping. 相似文献
8.
陈行堤 《数学年刊A辑(中文版)》2007,(4)
研究BA延拓和调和映照的关系,首先,给出了BA延拓为双曲调和的一个必要条件,特别地,若边界对应h局部是C~2和奇的,则其BA延拓不是双曲调和的。其次,证明了若h是分段C~2的则其BA延拓不是π调和的,除非h(x)=ax b,x∈R. 相似文献
9.
David Kalaj 《Mathematische Zeitschrift》2008,260(2):237-252
Let Ω and Ω1 be Jordan domains, let μ ∈ (0, 1], and let be a harmonic homeomorphism. The object of the paper is to prove the following results: (a) If f is q.c. and ∂Ω, ∂Ω1 ∈ C
1,μ
, then f is Lipschitz; (b) if f is q.c., ∂Ω, ∂Ω1 ∈ C
1,μ
and Ω1 is convex, then f is bi-Lipschitz; and (c) if Ω is the unit disk, Ω1 is convex, and ∂Ω1 ∈ C
1,μ
, then f is quasiconformal if and only if its boundary function is bi-Lipschitz and the Hilbert transform of its derivative is in
L
∞. These extend the results of Pavlović (Ann. Acad. Sci. Fenn. 27:365–372, 2002).
相似文献
10.
假设D是Rn(n2)中的区域,y=f(x):DRn是一个同胚.如果f(x)的模伸张K(x,f)适合条件A,则f(x)是ACL的. 相似文献
11.
Fang Ainong 《数学学报(英文版)》1998,14(4):473-480
Suppose thatD is a domain in
andy=f(x)∶D→R
n
is a homeomorphism. We prove that if the modulus dilatationK(x, f) satisfies the condition A thenf(x) is ACL.
Project supported by the National Natural Science Foundation of China and JTU 相似文献
12.
《Indagationes Mathematicae》2022,33(5):1061-1070
We prove that every quasiconformal mapping from the harmonic -Bloch space between the unit ball and a spatial domain with boundary is globally -Hölder continuous for , with the Hölder coefficient that does not depend neither on the mapping nor on . An analogous result also holds for Lipschitz continuous, quasiconformal harmonic mappings for . This is an approach towards the extension of some results from the complex plane obtained by Warschawski (1951) for conformal mappings and Kalaj (2022) for quasiconformal harmonic mappings. 相似文献
13.
Masahiro YANAGISHITA 《数学学报(英文版)》2014,(4)
Being a Strebel point gives a sufficient condition for that the extremal Beltrami coefficient is uniquely determined in a Teichmüller equivalence class.We consider how Strebel points are characterized.In this paper,we will give a new characterization of Strebel points in a certain subset of the universal Teichmüller space by a property of the Grunsky operator. 相似文献
14.
Tomeu Barcel Daniel Faraco Alberto Ruiz 《Journal de Mathématiques Pures et Appliquées》2007,88(6):522-556
It is proved that, in two dimensions, the Calderón inverse conductivity problem in Lipschitz domains is stable when the conductivities are Hölder continuous with any exponent α>0. 相似文献
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17.
1.IntroductionOnthegeometricfunctiontheoryofonecomplexvariable,thefollowinggrowthandi-coveringtheoremiswellknown(see[2]).TheoremA.Foreachno~alizedunivalentjunctionfontheunitdiscDCC,ESPecially,theleft-handsideOftheaboveinequalityimpliesf(D)2ID.ForeachzED,z/0,equalityoccursintheaboveinequalityifandonlyiffisKoe6efunctionK(z)=theoritsrotatione--"K(e"z).Itisnaturaltoextendthisandotherresultsonthegeometricfunctiontheoryofonevariablestoseveralvariables.Butasearlyasfiftyyearsago,H.Cartanpointe… 相似文献
18.
Keith Whittington 《Proceedings of the American Mathematical Society》1998,126(10):3131-3132
An elementary proof is given that if each pair of points of a homogeneous metric continuum can be mapped by a homeomorphism into an arbitrarily small connected set, then the continuum is locally connected.
19.
Xiaohui Zhang Gendi Wang Songliang Qiu 《Journal of Mathematical Analysis and Applications》2006,324(1):60-65
The authors prove a conjecture on elliptic integrals and obtain sharp bounds for φK(r) and λ(K). By using Teichmüller's module theorem, the authors obtain a distortion theorem of K-quasiconformal mappings on the plane. 相似文献
20.
张静 《高校应用数学学报(A辑)》2017,32(1)
给出连通的rectifiable空间是局部序列连通(或局部连通)的刻画,推广了拓扑群中的相应结果;利用rectifiable空间G中e的局部邻域基给出G是局部连通(或局部序列连通)的刻画;证明了若A是rectifiable空间G中的序列开子集,那么H=A是G的序列开rectifiable子空间. 相似文献