On conformal mapping of nearly circular regions

On Conformal Mapping of Nearly Circular Regions

Conformal Mapping of Right Circular Quadrilaterals

We study conformal mappings from the unit disk to circular-arc quadrilaterals with four right angles. The problem is reduced to a Sturm-Liouville boundary value problem on a real interval, with a nonlinear boundary condition, in which the coefficient functions contain the accessory parameters t, λ of the mapping problem. The parameter λ is designed in such a way that for fixed t, it plays the r...

Numerical conformal mapping of multiply connected domains to regions with circular boundaries

We propose a method to map a multiply connected bounded planar region conformally to a bounded region with circular boundaries. The norm of the derivative of such a conformal map satisfies the Laplace equationwith a nonlinear Neumann type boundary condition.We analyze the singular behavior at corners of the boundary and separate the major singular part. The remaining smooth part solves a variat...

On Conformal Mapping^of Regions Bounded by Smooth Curves

An explicit expression in terms of these parameters is obtained for AP. The fact that the integral in (3) remains bounded for 0^p<l under the assumption that C has continuously turning tangents was proved in an earlier paper of the writer [4, p. 362 j.1 The emphasis in the present note is upon the fact that the constant Ap depends only on the parameters indicated and is expressed explicitly in ...

Time-dependent conformal mapping of doubly-connected regions

This paper examines two key features of time-dependent conformal mappings in doubly-connected regions, the evolution of the conformal modulus Q(t) and the boundary transformation generalizing the Hilbert transform. It also applies the theory to an unsteady free surface flow. Focusing on inviscid, incompressible, irrotational fluid sloshing in a rectangular vessel, it is shown that the explicit ...