On conformal mapping of polygonal domains

Analysis and design of polygonal resistors by conformal mapping

To compute the electrical resistance ( ~ conformal modulus) of a polygonally shaped resistorcut from a sheet of uniform resistivity, it suffices to find a conformal map of the polygon onto arectangle. Constructing such a map requires the solution of a Schwarz-Christoffel parameter prob-lem. First we show by examples that this is practical numerically. Then we consider an inverse 704...

A General Theorem on Conformal Mapping of Multiply Connected Domains.

On conformal moduli of polygonal quadrilaterals

The change of conformal moduli of polygonal quadrilaterals under some geometric transformations is studied. We consider the motion of one vertex when the other vertices remain fixed, the rotation of sides, polarization, symmetrization, and averaging transformation of the quadrilaterals. Some open problems are formulated. 2000 Mathematics Subject Classification. Primary 30C85. Secondary 30C75.

Conformal Mapping of Long Quadrilaterals and Thick Doubly Connected Domains

Abstract. In this paper we investigate theoretically an approximation technique for avoiding the crowding phenomenon in numerical conformal mapping. The method applies to conformal maps from rectangles to "long quadrilaterals," i.e., Jordan domains bounded by two parallel straight lines and two Jordan arcs, where the two arcs are far apart. We require that these maps take the four corners of th...

On the Geodesic Centers of Polygonal Domains

In this paper, we study the problem of computing Euclidean geodesic centers of a polygonal domain P with a total of n vertices. We discover many interesting observations. We give a necessary condition for a point being a geodesic center. We show that there is at most one geodesic center among all points of P that have topologically-equivalent shortest path maps. This implies that the total numb...