The Bergman and Schiffer transforms on weighted norm spaces
The Bieberbach Conjecture for Restricted Initial Coefficients.
The Bieberbach Conjecture for Univalent Functions with Small Second Coefficients.
The boundary absolute continuity of quasiconformal mappings (II).
In this paper a quite complete picture is given of the absolute continuity on the boundary of a quasiconformal map B3 → D, where B3 is the unit 3-ball and D is a Jordan domain in R3 with boundary 2-rectifiable in the sense of geometric measure theory. Moreover, examples are constructed, for each n ≥ 3, showing that quasiconformal maps from the unit n-ball onto Jordan domains with boundary (n - 1)-rectifiable need not have absolutely continuous boundary values.
The Brothers Riesz theorem in and Laplace series.
The Carathéodory topology for multiply connected domains I
We consider the convergence of pointed multiply connected domains in the Carathéodory topology. Behaviour in the limit is largely determined by the properties of the simple closed hyperbolic geodesics which separate components of the complement. Of particular importance are those whose hyperbolic length is as short as possible which we call meridians of the domain. We prove continuity results on convergence of such geodesics for sequences of pointed hyperbolic domains which converge in the Carathéodory...
The Carathéodory topology for multiply connected domains II
We continue our exposition concerning the Carathéodory topology for multiply connected domains which we began in [Comerford M., The Carathéodory topology for multiply connected domains I, Cent. Eur. J. Math., 2013, 11(2), 322–340] by introducing the notion of boundedness for a family of pointed domains of the same connectivity. The limit of a convergent sequence of n-connected domains which is bounded in this sense is again n-connected and will satisfy the same bounds. We prove a result which establishes...
The Cauchy Kernel, the Szegö Kernel, and the Riemann Mapping Function.
The class of functions convex in the negative direction of the imaginary axis of order .
The class of functions spirallike with respect to a boundary point.
The class of mappings with bounded specific oscillation, and integrability of mappings with bounded distortion on Carnot groups.
The classes of univalent functions connected with homographies
We define some new classes of univalent functions. The Schiffer differential equations are obtained for extremal functions from some of these classes.
The coefficient problem for functions with positive real part in a finitely connected domain
The coefficients of quasiconformality of tori in n-space.
The complement of a quasimöbius sphere is uniform.
The cone of nonnegative polynomials with nonnegative coefficients and linear operators preserving this cone
Let be the cone of real univariate polynomials of degree ≤ 2n which are nonnegative on the real axis and have nonnegative coefficients. We describe the extremal rays of this convex cone and the class of linear operators, acting diagonally in the standard monomial basis, preserving this cone.
The covering radius of a mapping and the multiplicity of a covering.
The critical strips of the sums .
The Differential of a Quasi-conformal Mapping of a Carnot-Caratheodry Space.
The Dirichlet space: a survey.