Quasiconformal Analogues of a Theorem of Smirnov.
Quasiconformal dimensions of self-similar fractals.
The Sierpinski gasket and other self-similar fractal subsets of Rd, d ≥ 2, can be mapped by quasiconformal self-maps of Rd onto sets of Hausdorff dimension arbitrarily close to one. In R2 we construct explicit mappings. In Rd, d ≥ 3, the results follow from general theorems on the equivalence of invariant sets for iterated function systems under quasisymmetric maps and global quasiconformal maps. More specifically, we present geometric conditions ensuring that (i) isomorphic systems have quasisymmetrically...
Quasiconformal equivalence of spherical CR manifolds.
Quasiconformal groups acting on that are not quasiconformally conjugate to Möbius groups.
Quasiconformal groups of compact type.
We establish that a quasiconformal group is of compact type if and only if its limits set is purely conical and find that the limit set of a quasiconformal group of compact type is uniformly perfect. A key tool is the result of Bowditch-Tukia on compact-type convergence groups. These results provide crucial tools for studying the deformations of quasiconformal groups and in establishing isomorphisms between such groups and conformal groups.
Quasiconformal images of Hölder domains.
Quasiconformal mappings and asymptotic geometry of manifolds.
Quasiconformal mappings and Sobolev spaces
We examine how Poincaré change under quasiconformal maps between appropriate metric spaces having the same Hausdorff dimension. We also show that for many metric spaces the Sobolev functions can be identified with functions satisfying Poincaré, and this allows us to extend to the metric space setting the fact that quasiconformal maps from onto preserve the Sobolev space .
Quasiconformal mappings onto John domains.
In this paper we study quasiconformal homeomorphisms of the unit ball B = Bn = {x ∈ Rn: |x| < 1} of Rn onto John domains. We recall that John domains were introduced by F. John in his study of rigidity of local quasi-isometries [J]; the term John domain was coined by O. Martio and J. Sarvas seventeen years later [MS]. From the various equivalent characterizations we shall adapt the following definition based on diameter carrots, cf. [V4], [V5], [NV].
Quasiconformal mappings which increase dimension.
Quasiconformal mappings with Sobolev boundary values
We consider quasiconformal mappings in the upper half space of , , whose almost everywhere defined trace in has distributional differential in . We give both geometric and analytic characterizations for this possibility, resembling the situation in the classical Hardy space . More generally, we consider certain positive functions defined on , called conformal densities. These densities mimic the averaged derivatives of quasiconformal mappings, and we prove analogous trace theorems for them....
Quasiconformality and equivalent norms
We study the behaviour of a quasiconformal mapping when we change the norms of the considered normed spaces by other equivalent norms. We propose a new metric definition with which we can study the interdependence between a quasiconformal homeomorphism and the new equivalent norms of the normed spaces.
Quasiconformality and quasisymmetry in metric measure spaces.
Quasiconvex functions and null Lagrangians in the stability problems of classes of mappings.
Quasiharmonic fields
Quasiharmonic fields and Beltrami operators
A quasiharmonic field is a pair of vector fields satisfying , , and coupled by a distorsion inequality. For a given , we construct a matrix field such that . This remark in particular shows that the theory of quasiharmonic fields is equivalent (at least locally) to that of elliptic PDEs. Here we stress some properties of our operator and find their applications to the study of regularity of solutions to elliptic PDEs, and to some questions of G-convergence.
Quasihomographies in the theory of Teichmüller spaces [Book]
Quasiregular mappings of the Heisenberg group.
Quasiregular semigroups.
Quasi-Symmetric and quasi-Möbius maps on locally convex space.