On extremal quasiconformal extensions of conformal mappings

Letf(t, z)=z+tω(1/z) be schlicht for ⋎z⋎>1, ω(z) = Σ _n ^{= 0/∞} a _n z ⁿ ,t>0. The paper considers first-order estimates for the dilatation of extremal quasiconformal extensions off ast→0. This work was initiated during the Special Year in Complex Analysis at the Technion, and was supported in parts by the Samuel Neaman Fund, the Forschungsinstitut für Mathematik, ETH, Zürich, and the National Science Foundation.     

Boundary properties of conformal and quasiconformal mappings of polygons

Novosibirsk. Translated fromSibirski Matematicheski Zhurnal, Vol. 33, No. 6, pp. 31–38, November–December, 1992.     

Holomorphic functions and quasiconformal mappings with smooth moduli

We discuss the implication , where f is a holomorphic function (resp., a quasiconformal mapping) on a domain (resp., ) and Λ_ω(G) is the Lipschitz space associated with a majorant ω.     

On a boundary correspondence for quasiconformal mappings of three-dimensional domains

Siberian Mathematical Journal -     

Removability of certain sets in the class of three-dimensional quasiconformal mappings

The removability is established, in the class of three-dimensional quasi-conformal mappings, of closed sets on sufficiently smooth curves.Translated from Matematicheskie Zametki, Vol. 7, No. 6, pp. 717–722, June, 1970.     

Unique extremality of quasiconformal mappings

In this paper, we study the conditions under which unique extremality of quasiconformal mappings occurs and provide a broader point of view of this phenomenon. Additional information is obtained by means of specialized constructions. In particular, we generalize the construction theorem in [BLMM], thus providing a more basic understanding of it. We also generalize the notion of unique extremality and give an analytic characterization of the generalized concept. Research partially supported by MNTRS, Serbia, Grant No. 144 020     

Equicontinuity of mean quasiconformal mappings

We establish the equicontinuity and normality of the families R ^Φ of ring Q(x)-homeomorphisms with integral-type restrictions ∫^Φ(Q(x))dm(x) < ∞ on a domain D ⊂ R ⁿ with n ≥ 2. The resulting conditions on Φ are not only sufficient but also necessary for the equicontinuity and normality of these families of mappings. We give some applications of these results to the Sobolev classes W _loc^1,n .     

On the extremality of quasiconformal mappings and quasiconformal deformations

Given a family of quasiconformal deformations such that has a uniform bound , the solution of the Löwner-type differential equation

is an -quasiconformal mapping. An open question is to determine, for each fixed , whether the extremality of is equivalent to that of . The note gives this a negative approach in both directions.