Results 251 to 260 of about 329,116 (290)

Some Remarks on a Distortion Theorem

Some Remarks on a Distortion Theorem
openaire   +1 more source

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 ...
ENRIQUE VILLAMOR
openaire   +2 more sources

Distortion theorems for convex mappings on homogeneous balls [PDF]

Journal of Mathematical Analysis and Applications, 2010
Let B be the open unit ball of a complex Banach space X and let B be homogeneous. We prove distortion results for normalized convex mappings f:B→X which generalize various finite dimensional distortion theorems and improve some infinite dimensional ones.
Hidetaka Hamada
exaly   +2 more sources

Some of the next articles are maybe not open access.

Related searches:

Distortion Theorems for Diffeomorphisms

Canadian Mathematical Bulletin, 1994
AbstractGeneralizations of the Koebe distortion theorem to a class of diffeomorphisms are given. They are applied to univalent harmonic mappings.
Hengartner, W., Poulin, D.
openaire   +1 more source

A note on the distortion theorem

Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials, 2017
The distortion theorem is a conditional statement that establishes the certain relations between the variation of the mean bond length and the variation of the valence of a central ion of a coordination polyhedron. It was found that in some principal cases the conditional part of the distortion theorem is not necessary.
openaire   +2 more sources

The growth theorem and distortion theorem of spirallike mappings on B p

Acta Mathematica Sinica, English Series, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Hao, Lu, Ke Ping, Zhang, Fang Fang
openaire   +2 more sources

A Distortion Theorem for Univalent Gap Series

Siberian Mathematical Journal, 2003
Summary: We prove a distortion theorem for conformal mappings of the unit disk for which \(\log f'\) is representable as the Hadamard gap series. This theorem implies in particular that such conformal mapping is `almost' bounded, i.e., for every \(\varepsilon >0\), there is a positive constant \(C_\varepsilon\) such that \(|f(z)|\geq C_\varepsilon (1 ...
openaire   +2 more sources

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 ...
openaire   +2 more sources

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(
openaire   +2 more sources

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 ...
openaire   +2 more sources