Some Inequalities Relating to Conformal Mapping upon Canonical Slit-domains
نویسنده
چکیده
(1) f = se(z) = z + — + • • • z and which maps D conformally and bi-uniformly upon a domain De of the f-plane bounded by n rectilinear slits each of which makes the angle 0 with the positive direction of the real axis. The domain De is itself also uniquely determined for each value of 0. In the present paper we shall derive two inequalities involving the coefficient a$ appearing in (1) and the outer measure A of the complement (with respect to the entire plane) of the domain D— that is, the greatest lower bound of the total area enclosed by a set of analytic curves surrounding the boundary continua. The first of these inequalities is the following :
منابع مشابه
Conformal Slit Mapping and Its Applications to Brain Surface Parameterization
We propose a method that computes a conformal mapping from a multiply connected mesh to the so-called slit domain, which consists of a canonical rectangle or disk in which 3D curved landmarks on the original surfaces are mapped to concentric or parallel lines in the slit domain. In this paper, we studied its application to brain surface parameterization. After cutting along some landmark curve ...
متن کاملComputing Conformal Maps onto Canonical Slit Domains
We extend the results of [2] by computing conformal maps onto the canonical slit domains in Nehari [14]. Along the way, we demonstrate the computability of solutions to Neuman problems.
متن کاملGeneralization of the Schwarz-Christoffel mapping to multiply connected polygonal domains.
A generalization of the Schwarz-Christoffel mapping to multiply connected polygonal domains is obtained by making a combined use of two preimage domains, namely, a rectilinear slit domain and a bounded circular domain. The conformal mapping from the circular domain to the polygonal region is written as an indefinite integral whose integrand consists of a product of powers of the Schottky-Klein ...
متن کاملNumerical conformal mapping and its inverse of unbounded multiply connected regions onto logarithmic spiral slit regions and straight slit regions.
This paper presents a boundary integral equation method with the adjoint generalized Neumann kernel for computing conformal mapping of unbounded multiply connected regions and its inverse onto several classes of canonical regions. For each canonical region, two integral equations are solved before one can approximate the boundary values of the mapping function. Cauchy's-type integrals are used ...
متن کاملConformal Mapping of Unbounded Multiply Connected Regions onto Canonical Slit Regions
and Applied Analysis 3 ΓM Γ2 Γ1
متن کامل