The Asymptotic Value of the Circle-Packing Rigidity Constants sn .
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 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 extreme points of a class of functions with positive real part.
The linear topological quasiconformality coefficient and sufficient conditions for the branch points of mappings.
The mapping by heights for quadratic differentials in the disk.
The Poisson extension of K -quasihomography on the unit circle
In this paper some estimates for the Poisson extension of a K-quasihomography on the unit circle are given.