Differentiability of the mappings of Carnot-Carathéodory spaces in the Sobolev and -topologies.
Dimensions conformes, espaces Gromov-hyperboliques et ensembles autosimilaires
Doubling measures and quasiconformal maps.
Elliptic complexes in the calculus of variations [Book]
Embedding theorems for Bergman spaces in quasiconformal balls.
Equicontinuous classes of ring -homeomorphisms.
Equivalence of the Apollonian and its inner metric.
Essential singularities of quasimeromorphic mappings.
Estimates for the energy integral of quasiregular mappings on Riemannian manifolds and isoperimetry
The rate of growth of the energy integral of a quasiregular mapping is estimated in terms of a special isoperimetric condition on . The estimate leads to new Phragmén-Lindelöf type theorems.
Euclidean quasiconvexity.
Exhaustions of John domains.
Existence of quasi-isometric mappings and Royden compactifications.
Extension of bilipschitz maps of compact polyhedra.
Extreme points of subordination and weak subordination families of harmonic mappings
The aim of the paper is to discuss the extreme points of subordination and weak subordination families of harmonic mappings. Several necessary conditions and sufficient conditions for harmonic mappings to be extreme points of the corresponding families are established.
Fine topology and -harmonic morphisms.
Fixed points of composite entire and quasiregular maps.
Functional identities for special functions of quasiconformal theory.
Generalized dimension compression under mappings of exponentially integrable distortion
We prove a dimension compression estimate for homeomorphic mappings of exponentially integrable distortion via a modulus of continuity result by D. Herron and P. Koskela [Mappings of finite distortion: gauge dimension of generalized quasicircles, Illinois J. Math., 2003, 47(4), 1243–1259]. The essential sharpness of our estimate is demonstrated by an example.
Generalized John disks
We establish the basic properties of the class of generalized simply connected John domains.
Generalized mean porosity and dimension.