Quasihomographies in the theory of Teichmüller spaces

Zając Józef

Displaying similar documents to “Quasihomographies in the theory of Teichmüller spaces”

Loewner chains and quasiconformal extension of holomorphic mappings

Hidetaka Hamada, Gabriela Kohr (2003)

Annales Polonici Mathematici

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Let f(z,t) be a Loewner chain on the Euclidean unit ball B in ℂⁿ. Assume that f(z) = f(z,0) is quasiconformal. We give a sufficient condition for f to extend to a quasiconformal homeomorphism of $ℝ^{2 n}$ onto itself.

Uniform convergence of the generalized Bieberbach polynomials in regions with zero angles

F. G. Abdullayev (2001)

Czechoslovak Mathematical Journal

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Let $C$ be the extended complex plane; $G \subset C$ a finite Jordan with $0 \in G$ ; $w = ϕ (z)$ the conformal mapping of $G$ onto the disk $B (0; ρ_{0}) : = \}w |w| < ρ_{0}\{$ normalized by $ϕ (0) = 0$ and $ϕ^{'} (0) = 1$ . Let us set $ϕ_{p} (z) : = \int_{0}^{z} {[ϕ^{'} (ζ)]}^{2 / p} d ζ$ , and let $π_{n, p} (z)$ be the generalized Bieberbach polynomial of degree $n$ for the pair $(G, 0)$ , which minimizes the integral $\underset{G}{\int \int} {|ϕ_{p}^{'} (z) - P_{n}^{'} (z)|}^{p} d σ_{z}$ in the class of all polynomials of degree not exceeding $\leq n$ with $P_{n} (0) = 0$ , $P_{n}^{'} (0) = 1$ . In this paper we study the uniform convergence of the generalized Bieberbach polynomials $π_{n, p} (z)$ to $ϕ_{p} (z)$ on $\bar{G}$ with interior and exterior zero angles and determine its dependence...

Regularity theorems for solutions of partial differential equations for quasiconformal mappings in several dimensions

Tadeusz Iwaniec

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CONTENTSPreliminaries........................................................................................................ 51. Auxiliary results......................................................................................................... 132. The second order equations.................................................................................. 143. Some properties of Sobolev and Besov spaces................................................ 204. Classes $Λ^{α} (G, H)$ , 0 < a...

Harmonic mappings in the exterior of the unit disk

Magdalena Gregorczyk, Jarosław Widomski (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this paper we consider a class of univalent orientation-preserving harmonic functions defined on the exterior of the unit disk which satisfy the condition $\sum_{n = 1}^{\infty} n^{p} (| a_{n} | + | b_{n} |) \leq 1$ . We are interested in finding radius of univalence and convexity for such class and we find extremal functions. Convolution, convex combination, and explicit quasiconformal extension for this class are also determined.

The generalized Neumann-Poincaré operator and its spectrum

Partyka Dariusz

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CONTENTSIntroduction..........................................................................................................................................................................5Preliminaries. Complex harmonic functions..........................................................................................................................7I. Spectral values and eigenvalues of a Jordan curve........................................................................................................19 1.1....

The boundary absolute continuity of quasiconformal mappings (II).

Juha Heinonen (1996)

Revista Matemática Iberoamericana

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In this paper a quite complete picture is given of the absolute continuity on the boundary of a quasiconformal map B → D, where B is the unit 3-ball and D is a Jordan domain in R with boundary 2-rectifiable in the sense of geometric measure theory. Moreover, examples are constructed, for each n ≥ 3, showing that quasiconformal maps from the unit n-ball onto Jordan domains with boundary (n - 1)-rectifiable need not have absolutely continuous boundary values.

Quasiconformal mappings and exponentially integrable functions

Fernando Farroni, Raffaella Giova (2011)

Studia Mathematica

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We prove that a K-quasiconformal mapping f:ℝ² → ℝ² which maps the unit disk onto itself preserves the space EXP() of exponentially integrable functions over , in the sense that u ∈ EXP() if and only if $u \circ f^{- 1} \in E X P ()$ . Moreover, if f is assumed to be conformal outside the unit disk and principal, we provide the estimate $1 / (1 + K l o g K) \leq (| | u \circ f^{- 1} {| |}_{E X P ()} {) / (| | u | |}_{E X P ()}) \leq 1 + K l o g K$ for every u ∈ EXP(). Similarly, we consider the distance from $L^{\infty}$ in EXP and we prove that if f: Ω → Ω’ is a K-quasiconformal mapping and G ⊂ ⊂ Ω, then $1 / K \leq (d i s t_{E X P (f (G))} (u \circ f^{- 1}, L^{\infty} (f (G)))) / (d i s t_{E X P (f (G))} (u, L^{\infty} (G))) \leq K$ for every u ∈ EXP(). We also...

Invertible harmonic mappings beyond the Kneser theorem and quasiconformal harmonic mappings

David Kalaj (2011)

Studia Mathematica

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We extend the Rado-Choquet-Kneser theorem to mappings with Lipschitz boundary data and essentially positive Jacobian at the boundary without restriction on the convexity of image domain. The proof is based on a recent extension of the Rado-Choquet-Kneser theorem by Alessandrini and Nesi and it uses an approximation scheme. Some applications to families of quasiconformal harmonic mappings between Jordan domains are given.

Eine Klasse nichtschlichter konformer Abbildungen mit einer schlichten quasikonformen Fortsetzung. II

Reiner Kühnau (2011)

Annales UMCS, Mathematica

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We study a dual analogue of the class Σ(κ) of hydrodynamically normalized schlicht conformal mappings g(z) of the exterior of the unit circle with a [...] -quasiconformal extension, namely now those (non-schlicht) mappings g(z) for which g(z) has such a quasiconformal extension.