Über die quasikonforme Fortsetzung schlichter Funktionen.
Über eine Golusinsche Ungleichung für quasikonform fortsetzbare schlichte Funktionen.
Über Integraltransformationen, die analytische Funktionen in Lösungen elliptischer Differentialgleichungssysteme überführen
Ueber extremale quasikonforme Abbildungen.
Uniformly quasiregular semigroups in two dimensions.
Univalent functions and the Schwarzian derivative.
Univalent functions with logarithmic restrictions
It is known that univalence property of regular functions is better understood in terms of some restrictions of logarithmic type. Such restrictions are connected with natural stratifications of the studied classes of univalent functions. The stratification of the basic class S of functions regular and univalent in the unit disk by the Grunsky operator norm as well as the more general one of the class 𝔐 * of pairs of univalent functions without common values by the τ-norm (this concept is introduced...
Univalent -harmonic mappings : applications to composites
This paper is part of a larger project initiated with [2]. The final aim of the present paper is to give bounds for the homogenized (or effective) conductivity in two dimensional linear conductivity. The main focus is therefore the periodic setting. We prove new variational principles that are shown to be of interest in finding bounds on the homogenized conductivity. Our results unify previous approaches by the second author and make transparent the central role of quasiconformal mappings in all...
Univalent σ-harmonic mappings: applications to composites
This paper is part of a larger project initiated with [2]. The final aim of the present paper is to give bounds for the homogenized (or effective) conductivity in two dimensional linear conductivity. The main focus is therefore the periodic setting. We prove new variational principles that are shown to be of interest in finding bounds on the homogenized conductivity. Our results unify previous approaches by the second author and make transparent the central role of quasiconformal mappings in all...
Universal Teichmüller space and Fourier series.
Variability sets on Riemann surfaces and forgetful maps between Teichmüller spaces.
Variation of quasiconformal mappings on lines
We obtain improved regularity of homeomorphic solutions of the reduced Beltrami equation, as compared to the standard Beltrami equation. Such an improvement is not possible in terms of Hölder or Sobolev regularity; instead, our results concern the generalized variation of restrictions to lines. Specifically, we prove that the restriction to any line segment has finite p-variation for all p > 1 but not necessarily for p = 1.
Versions of Koebe 1/4 Theorem for Analytic and Quasiregular Harmonic Functions and Applications
Verzerrungsaussagen bei quasikonformen Abbildungen mit ortsabhängiger Dilationsbeschränkung und ein Extremalprinzip der Elektrostatik in inhomogenen Medien.
Wandering domains and invariant conformal structures for mappings of the 2-torus.
Wann sind die Grunskyschen Koeffizientenbedingungen hinreichend für Q-quasikonforme Fortsetzbarkeit?
Weak Chord-Arc Curves and Double-Dome Quasisymmetric Spheres
Let Ω be a planar Jordan domain and α > 0. We consider double-dome-like surfaces Σ(Ω, tα) over Ω where the height of the surface over any point x ∈ Ωequals dist(x, ∂Ω)α. We identify the necessary and sufficient conditions in terms of and α so that these surfaces are quasisymmetric to S2 and we show that Σ(Ω, tα) is quasisymmetric to the unit sphere S2 if and only if it is linearly locally connected and Ahlfors 2-regular.
Weakly starlike logharmonic mappings.
Wiman and Arima theorems for quasiregular mappings.
Zur Methode der Randintegration bei quasikonformen Abbildungen