Représentation conforme et symétries: une détermination élémentaire du module d'un quadrilatère en forme de L.
Rigidity of circle domains whose boundary has ...-finite linear measure.
-plane analysis for the fundamental problems of a stretched infinite plate weakened by curvilinear holes.
Schwarzovy-Christoffelovy integrály
Second Derivatives of Circle Packings and Conformai Mappings.
Sharp estimates of the curvature of some free boundaries in two dimensions.
Short separating geodesics for multiply connected domains
We consider the following questions: given a hyperbolic plane domain and a separation of its complement into two disjoint closed sets each of which contains at least two points, what is the shortest closed hyperbolic geodesic which separates these sets and is it a simple closed curve? We show that a shortest geodesic always exists although in general it may not be simple. However, one can also always find a shortest simple curve and we call such a geodesic a meridian of the domain. We prove that,...
Sine - Laplace Equation, Sinh-Laplace Equation and Harmonic Maps.
Smirnov domains
Some characterizations of harmonic Bloch and Besov spaces
The relationship between weighted Lipschitz functions and analytic Bloch spaces has attracted much attention. In this paper, we define harmonic --Bloch space and characterize it in terms of and where is a majorant. Similar results are extended to harmonic little --Bloch and Besov spaces. Our results are generalizations of the corresponding ones in G. Ren, U. Kähler (2005).
Some Extremal Problems for Functions Univalent in an Annulus.
Stabilität konformer Verheftung.
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 hyperbolic metric in a rectangle. II.
The hyperbolic metric of a rectangle.
The Löwner-Kufarev representations for domains with analytic boundaries
We consider the Löwner-Kufarev differential equations generating univalent maps of the unit disk onto domains bounded by analytic Jordan curves. A solution to the problem of the maximal lifetime shows how long a representation of such functions admits using infinitesimal generators analytically extendable outside the unit disk. We construct a Löwner-Kufarev chain consisting of univalent quadratic polynomials and compare the Löwner-Kufarev representations of bounded and arbitrary univalent functions....
The radius of univalence and starlikeness of some classes of regular functions
The Schwarz-Christoffel conformal mapping for “polygons” with infinitely many sides.
The Schwarz-Christoffel conformal mapping for "polygons" with infinitely many sides.