Conformal and generalized concircular mappings of Einstein-Weyl manifolds

In this article, after giving a necessary and sufficient condition for two Einstein-Weyl manifolds to be in conformal correspondence, we prove that any conformal mapping between such manifolds is generalized concircular if and only if the covector field of the conformal mapping is locally a gradient. Using this fact we deduce that any conformal mapping between two isotropic Weyl manifolds is a generalized concircular mapping. Moreover, it is shown that a generalized concircularly flat Weyl manifold is generalized concircular to an Einstein manifold and that its scalar curvature is prolonged covariant constant.     

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.     

Symmetrization, Green's function, and conformal mappings

Let h(zξ)−log|z−ξ| be the Green function of a planar domain D. The behavior of the linear combination h(z,z)+h(ξ,ξ)−2h(z,ξ) under certain symmetrization transformations of D is studied. Covering and distortion theorems in the theory of univalent functions are proved as applications. Bibliography: 9 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 80–92.     

On mappings related to the gradient of the conformal radius

We establish a criterion for the gradient ?R(D, z) of the conformal radius of a convex domain D to be conformal: the boundary ?D must be a circle. We obtain estimates for the coefficients K(r) for the K(r)-quasiconformal mappings ?R(D, z), D(r) ? D, 0 < r < 1, and supplement the results of Avkhadiev and Wirths concerning the structure of the boundary under diffeomorphic mappings of the domain D.     

On the curved wedge condition and the continuity moduli of conformal mappings

A Jordan curveL is studied, which satisfies an interior or exterior wedge condition for wedges of various geometric forms. We obtain estimates of the continuity moduli for the conformal mappings of the exterior (interior) ofL onto the exterior (interior) of the unit disk.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 6, pp. 763–769, June, 1993.     

On stability of classes of conformal mappings. I

Dedicated to the blessed memory of Ivan Nikolaevich Pesin.     

On spin and modularity in conformal field theory

We shall investigate chiral conformal field theories with 1-dimensional conformal anomalies with or without spin. We shall rigorously classify such anomalies and describe their modularity properties. Thereby, we give a detailed mathematical treatment of the simplest case of G. Segal's approach to conformal field theory.