Hardy spaces, A..., and singular integrals on chord-arc domains
Hausdorff dimension and quasisymmetric mappings.
Hebbare Singularitäten quasikonformer Abbildungen und lokal beschränkter holomorpher Funktionen.
Hölder continuity of conformal mappings and non-quasiconformal Jordan curves.
Holomorphic motions commuting with semigroups
A holomorphic family , |z|<1, of injections of a compact set E into the Riemann sphere can be extended to a holomorphic family of homeomorphisms , |z|<1, of the Riemann sphere. (An earlier result of the author.) It is shown below that there exist extensions which, in addition, commute with some holomorphic families of holomorphic endomorphisms of , |z|<1 (under suitable assumptions). The classes of covering maps and maps with the path lifting property are discussed.
Injectivity of local quasi-isometries.
Invertible harmonic mappings beyond the Kneser theorem and quasiconformal harmonic mappings
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.
Isometrische und Konforme Verheftung
Jørgensen's inequality for discrete convergence groups.
Kleinian groups, the Teichmueller space and Mostow's rigidity theorem.
Koebe Arcs and Quasiregular Mappings.
Konforme Verheftung von Gebieten mit beschränkter Randdrehung.
Konvergenzbetrachtungen bei quasikonformen Abbildungen im ... mittels Sätzen von K. Strebel
Konvergenzsätze für Jacobi-Determinanten von n-dimensionalen quasikonformen Abbildungen
Length of curves under conformal mappings.
Lindelöf-type theorems for quasiconformal and quasiregular mappings
Linear dilatation and absolute continuity.
Löwnersche Differentialgleichung und quasikonform fortsetzbare schlichte Funktionen.
Löwnersche Differentialgleichung und Schlichtheitskriterien.
Mappings of finite distortion: formation of cusps.
In this paper we consider the extensions of quasiconformal mappings f: B → Ωs to the whole plane, when the domain Ωs is a domain with a cusp of degree s > 0 and thus not an quasidisc. While these mappings do not have quasiconformal extensions, they may have extensions that are homeomorphic mappings of finite distortion with an exponentially integrable distortion, but in such a case ∫2B exp(λK(x)) dx = ∞ for all λ > 1/s. Conversely, for a given s > 0 such a mapping is constructed...