Results 281 to 290 of about 1,722,948 (307)

UNIQUENESS THEOREMS FOR MAPPINGS OF FINITE DISTORTION

Journal of the Australian Mathematical Society, 2017
In this paper we prove uniqueness theorems for mappings $F\in W_{\text{loc}}^{1,n}(\mathbb{B}^{n};\mathbb{R}^{n})$ of finite distortion $1\leq K(x)=\Vert \mathit{DF}(x)\Vert ^{n}/J_{F}(x)$ satisfying some integrability conditions. These types of theorems fundamentally state that if a mapping defined in $\mathbb{B}^{n}$ has the same boundary limit $a ...
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DISTORTION THEOREMS FOR BOUNDED UNIVALENT FUNCTIONS

Analysis, 2003
Let be \[ D_hf(z) = \frac{1-| z| ^2}{1-| f(z)| ^2}f'(z) \] for a conformal map \(f(z)\) from the unit disk into itself. It was proved by \textit{W. Ma} and \textit{D. Minda} [Ann. Acad. Sci. Fenn., Math. 22, 425 - 444 (1997; Zbl 0908.30016)] \[ \Big(\Big(\frac{| D_hf(z_1)| }{1-| D_hf(z_1)| }\Big)^p + \Big(\frac{| D_hf(z_2)| }{1-| D_hf(z_2)| }\Big)^p ...
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Distortion theorems for polynomials on a circle

Sbornik: Mathematics, 2000
The author considers polynomials \[ P(z)= \sum^n_{k=0} c_kz^k, \quad c_n\neq 0, \] for points \(z=e^{i\varphi}\) on the unit circle. He proves new and interesting estimates for the derivatives \[ {\partial\text{Re} P(e^{i \varphi}) \over\partial \varphi},\;{\partial\bigl|P(e^{i\varphi}) \bigr |^2 \over\partial\varphi} \text{ and } {\partial\arg \bigl(P(
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An extension of the Ahlfors distortion theorem

Mathematical Proceedings of the Cambridge Philosophical Society, 1954
1. The conformal mapping of a strip domain in the z-plane on to a parallel strip— parallel, say, to the real axis of the ζ ( = ξ + iμ)-plane—brings about a certain distortion. More precisely: consider a cross-cut on the line ℜz = c joining the two sides of the frontier of the strip domain (in these introductory remarks we suppose for simplicity that ...
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A distortion theorem for close-to-convex functions

1991
The author proves that if the function \(f(z)\) is in the usual class of close-to-convex functions and if \(| z ...
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Lemniscate Zone and Distortion Theorems for Multivalent Functions

Journal of Mathematical Sciences, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Bloch’s theorem for mappings of bounded and finite distortion

Mathematische Annalen, 2007
The author of the paper under review studies covering properties of mappings of bounded and exponentially integrable distortion on the unit ball of \({\mathbb R}^n\) and proves Bloch-type theorems.
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General Distortion Theorem for Univalent Functions with Quasiconformal Extension

, 2017
S. Krushkal
semanticscholar   +1 more source

Distortion Theorem for Locally Biholomorphic Bloch Mappings on the Unit Ball $$\mathcal {B}^{n*}$$Bn∗

, 2015
Jianfei Wang
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A Distortion Theorem for Functions Convex in One Direction

, 2011
M. Elin, D. Shoikhet, Fiana Yacobzon
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