and Notation.- Moduli and Capacity.- Moduli and Domains.- Q-Homeomorphisms with Q? Lloc1.- Q-homeomorphisms with Q in BMO.- More General Q-Homeomorphisms.- Ring Q-Homeomorphisms.- Mappings with Finite Length Distortion (FLD).- Lower Q-Homeomorphisms.- Mappings with Finite Area Distortion.- On Ring Solutions of the Beltrami Equation.- Homeomorphisms with Finite Mean Dilatations.- On Mapping Theory in Metric Spaces.

/pdf/moduli-in-modern-mapping-theory-4toq7octvy.pdf

Moduli in Modern Mapping Theory

Generalized Analytic Functions. By I. N. Vekua. English Translation Editor I. N. Sneddon. Pergamon Press. 1962. Pp. 668. 105s.

/pdf/toward-the-theory-of-orlicz-sobolev-classes-h1teavt299.pdf

Toward the theory of Orlicz–Sobolev classes

We prove the existence and uniqueness of homeomorphic ACL solutions to the Beltrami equation in the case when the dilatation coefficient of the equation has a majorant of finite mean oscillation.

Finite mean oscillation and the Beltrami equation

http://www.maths.qmul.ac.uk/%7Eob/publ/decay31.pdf

Explicit eigenvalue estimates for transfer operators acting on spaces of holomorphic functions

Chapter 17 - Foundations of Quasiconformal Mappings

This survey paper presents in the 2-dimensional case recent results which generalize plane quasiconformality and quasiregularity to the case of mappings whose distortion is dominated by a BMO-function. These are the so-called BMO-mappings. After a brief exposure on real BMO-functions in §2 classes of BMO-mappings are discussed in §3. §4 is devoted to BMO — QC and -QR mappings in the sense of Ryazanov, Srebro and Yakubov, and §4 to BMO-BD considered by Astala, Iwanie0107;, Koskela and Martin. BMO-mappings between Riemann and Klein surfaces are discussed in §4.5.

BMO-Mappings in the Plane

Theorie der Funktionen mehrerer komplexer Veränderlicher

Partial differential equations related to extremal problems for quasiconformal mappings

In the frame of the vast literature on the definitions of the quasiconformality, there are many papers dedicated to the reduction as much as possible of the conditions imposed on the homeomorphisms in order that they be quasiconformal. For example we quote only the joint paper of F. W. Gehring and J. V~is~l~ [i0], or in the n-dimensional case the papers of J. V~is~l~ [13] and of P. Caraman [8]. (See also [9] Part 2, and [14] Sections 13, 34, 36). We shall present here other results in the same direction. Starting from our paper [3] we established in [5] connections between Gr~tzsch's and Rengel's inequalities in the n-dimensional case. Now we shall develop these connections and obtain consequences for the quasiconformality coefficient and a quasiconformality criterium assuming that Gr~tzsch's inequality is verified only for certain families of q-surfaces, which define by their module the q-module of a topological n-cube. As usually q = 1,2,...,n 1 and the case q = 1 corresponds to the curves. In this preliminary paragraph we remind some definitions and results proved in [5] which will be basic facts for this paper. We shall work with the classical module of families of q-surfaces, using the following

Cabiria Andreian Cazacu

Papers

Chapter 17 - Foundations of Quasiconformal Mappings

BMO-Mappings in the Plane

Theorie der Funktionen mehrerer komplexer Veränderlicher

Partial differential equations related to extremal problems for quasiconformal mappings

On the Grötzsch and Rengel inequalities