共查询到20条相似文献,搜索用时 15 毫秒
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In this paper, the authors introduce a definition of the Schwarzian derivative of any locally univalent harmonic mapping defined on a simply connected domain in the complex plane. Using the new definition, the authors prove that any harmonic mapping f which maps the unit disk onto a convex domain has Schwarzian norm ■≤ 6. Furthermore, any locally univalent harmonic mapping f which maps the unit disk onto an arbitrary regular n-gon has Schwarzian norm■. 相似文献
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利用函数论的一般方法给出单位圆盘到自身的调和映照的傅立叶系数的界限,改进并推广了P.Duren和王晓英的相关结果. 相似文献
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In this paper, we investigate Clunie and Sheil-Small’s covering theorems for sense-preserving planar harmonic univalent mappings defined in the unit disk. Our results significantly improve the earlier known result. Also, we obtain a distortion theorem for fully starlike harmonic mappings in the unit disk. 相似文献
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《复变函数与椭圆型方程》2012,57(2):81-92
Functions f in the class $ K_H $ are convex, univalent, harmonic, and sense preserving in the unit disk. Such functions can be expressed as $ f = h + \overline {g} $ where h and g are analytic functions. If $ f \in K_H $ has $ h(0) = 0, g(0) = 0, h'(0) = 1$ , and $ g'(0) = 0 $ , then $ f \in K_H^0 $ . For $ f \in K_H^0 $ and } analytic in the unit disk, an integral representation for $ f\tilde {*}\varphi = h*\varphi + \overline {g*\varphi } $ is found. With } a strip mapping, $ f\tilde {*}\varphi $ is shown to be in $ K_H^0 $ . In a 1958 paper, Pólya and Schoenberg conjectured that if f and g are conformal mappings of the unit disk onto convex domains, then the Hadamard product f 2 g of f and g has the same property. It is known that the analogue of that result for harmonic mappings is false. In this paper, some examples are given in which the property of convexity is preserved for Hadamard products of certain convex harmonic mappings. In addition, an integral formula is used to determine the geometry of the Hadamard product from the geometry of the factors. This is true in particular for the convolution of strip mappings with certain functions $ f_n \in K_H^0 $ which take the unit disk to regular n -gons. 相似文献
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Mengkun Zhu & Xinzhong Huang 《数学研究》2015,48(3):265-274
Some sharp estimates for coefficients, distortion and the growth order are
obtained for harmonic mappings $f ∈ TL^α_H$which are locally univalent harmonic mappings
in the unit disk $\mathbb{D}:=\{z:|z| < 1\}$. Moreover, denoting the subclass $TS^α_H$ of the
normalized univalent harmonic mappings, we also estimate the growth of $|f|,$ $f ∈ TS^α_H,$ and their covering theorems. 相似文献
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Mengkun Zhu & Xinzhong Huang 《数学研究》2016,49(1):23-32
Some sharp estimates for coefficients, distortion and the growth order are
obtained for harmonic mappings $f \in TL^{\alpha}_H,$ which are locally univalent harmonic mappings
in the unit disk $\mathbb{D}:=\{z:|z|<1\}.$ Moreover, denoting the subclass $TS^{\alpha}_H$ of the
normalized univalent harmonic mappings, we also estimate the growth of $|f|,$ $f \in TS^α_H,$ and their covering theorems. 相似文献
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In this paper, we consider the class of uniformly locally univalent harmonic mappings in the unit disk and build a relationship between its pre-Schwarzian norm and uniformly hyperbolic radius. Also, we establish eight ways of characterizing uniformly locally univalent sense-preserving harmonic mappings. We also present some sharp distortions and growth estimates and investigate their connections with Hardy spaces. Finally, we study subordination principles of norm estimates. 相似文献
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In this paper,we discuss the sense-preserving univalent harmonic mappings from the unit disk D onto asymmetrical vertical strips Ω_α={ω:α-π/2sinαR(ω)α/2sinα},π/2≤απSuch results as analytic representation formula,coefficient estimates,distortion theorem and area theorem are derived. 相似文献
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David Kalaj 《Monatshefte für Mathematik》2012,36(1):205-229
The conformal deformations are contained in two classes of mappings quasiconformal and harmonic mappings. In this paper we consider the intersection of these classes. We show that, every K quasiconformal harmonic mapping between surfaces with boundary is a Lipschitz mapping. This extends some recent results of several authors where the same problem has been considered for plane domains. As an application it is given an explicit Lipschitz constant of normalized isothermal coordinates of a disk-type minimal surface in terms of boundary curve only. It seems that this kind of estimates are new for conformal mappings of the unit disk onto a Jordan domain as well. 相似文献
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黄新民 《纯粹数学与应用数学》1998,14(4):89-94,84
本文对于给定的Betrami系数a(z)找到了存在将单位圆盘U映射为给定的多边形P并且满足方程fx^-=a(z)fx的单叶调和保向映射函数f(z)的条件。 相似文献
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Summary The idea initiated by Opfer for constructing conformal mappings from the disk onto starlike domains is generalized for univalent harmonic mappings. This is of some interest, since such mappings are not characterized by analytic means.This work was supported in partsby a Promotion of Research Grant from the TECHNION, Haifaby an Undergraduate Student Research A ward from the NSERCby grants from the NSERC and the FCAR 相似文献
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给定单位圆盘D={z||z|1}上调和映照f(z)=h(z)+g(z),其中h(z)和g(z)为D上的解析函数,满足f(0)=0,λf(0)=1,ΛfΛ.通过引入复参数λ,|λ|=1,本文研究调和映照Fλ(z)=h(z)+λg(z)和解析函数Gλ(z)=h(z)+λg(z)的性质,得到Fλ(z)和Gλ(z)单叶半径的精确估计.作为应用,本文得到单位圆盘D上某些K-拟正则调和映照Bloch常数的更好估计,改进和推广由Chen等人所得的相应结果. 相似文献
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The primary aim of this paper is to characterize the uniformly locally univalent harmonic mappings in the unit disk. Then, we obtain sharp distortion, growth and covering theorems for one parameter family \({{\mathcal {B}}}_{H}(\lambda )\) of uniformly locally univalent harmonic mappings. Finally, we show that the subclass of k-quasiconformal harmonic mappings in \({{\mathcal {B}}}_{H}(\lambda )\) and the class \({{\mathcal {B}}}_{H}(\lambda )\) are contained in the Hardy space of a specific exponent depending on \(\lambda \), respectively, and we also discuss the growth of coefficients for harmonic mappings in \({{\mathcal {B}}}_{H}(\lambda )\). 相似文献
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Allen Weitsman 《Proceedings of the American Mathematical Society》1998,126(2):447-452
It is shown that if is a univalent harmonic mapping of the unit disk onto a domain having a smooth boundary arc which is convex with respect to the domain, and if the dilatation has modulus 1 on the arc, then the arc must be a line segment.
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It is proved that every quasiconfomal harmonic mapping of the unit disk onto a surface with rectifiable boundary has absolutely
continuous extension to the boundary as well as its inverse mapping has this property. In addition it is proved an isoperimetric
type inequality for the class of these surfaces. These results extend some classical results for conformal mappings, minimal
surfaces and surfaces with constant mean curvature treated by Kellogg, Courant, Nitsche, Tsuji, F. Riesz and M. Riesz, etc. 相似文献
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