Normal families, multiplicity and the branch set of quasiregular maps.
On a theorem of Lindelöf
We give a quasiconformal version of the proof for the classical Lindelöf theorem: Let f map the unit disk D conformally onto the inner domain of a Jordan curve C. Then C is smooth if and only if arh f'(z) has a continuous extension to D. Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.
On conformal dilatation in space.
On harmonic quasiconformal quasi-isometries.
On Lipschitz continuity of harmonic quasiregular maps on the unit ball in .
On local injectivity and asymptotic linearity of quasiregular mappings
It is shown that the approximate continuity of the dilatation matrix of a quasiregular mapping f at implies the local injectivity and the asymptotic linearity of f at . Sufficient conditions for to behave asymptotically as are given. Some global injectivity results are derived.
On mappings with bounded distortion on Heisenberg group.
On pseudospheres that are quasispheres.
We construct bounded domains D not equal to a ball in n ≥ 3 dimensional Euclidean space, Rn, for which ∂D is homeomorphic to a sphere under a quasiconformal mapping of Rn and such that n - 1 dimensional Hausdorff measure equals harmonic measure on ∂D.
On -homeomorphisms.
On quasiregular polynomial mappings
On selfsimilar Jordan curves on the plane.
On some characterizations of quasiregularity
On the conformal gauge of a compact metric space
In this article we study the Ahlfors regular conformal gauge of a compact metric space , and its conformal dimension . Using a sequence of finite coverings of , we construct distances in its Ahlfors regular conformal gauge of controlled Hausdorff dimension. We obtain in this way a combinatorial description, up to bi-Lipschitz homeomorphisms, of all the metrics in the gauge. We show how to compute using the critical exponent associated to the combinatorial modulus.
On the dynamics of pseudo-Anosov homeomorphisms on representation varieties of surface groups.
On the relative Schoenflies theorem.
On the traces of Sobolev functions on the boundary of a cusp with a Hölder singularity.
Pathwise connectivity in uniform domains with small exceptional sets.
Periodic quasiregular mappings of finite order.
The authors construct a periodic quasiregular function of any finite order p, 1 < p < infinity. This completes earlier work of O. Martio and U. Srebro.
Properties of the mappings that are close to the harmonic mappings. II.
Quadruples and spatial quasiconformal mappings.