On a conformal-mapping property

On Moduli in Conformal Mapping.

Geometrically, the theorem states that if a variety U/k becomes birationally equivalent to an Abelian variety over the algebraic closure of k, then it is birationally equivalent to an Abelian variety over k. (If k is a field with a discrete valuation, and ir is a prime element, then the curve defined by the equation X" + 7rY" + 7r2Zn = 0, with n = 3, shows that the conclusion of the theorem doe...

Remarks on "some Problems in Conformal Mapping"

1. The present note contains several remarks on an earlier paper by the author [2].1 In Chapter IV, §4, which deals with the question of when we can have equality of modules for a triply-connected domain and a proper subdomain, the last sentence was added in proof. This accounts for the apparent disparity between it and the preceding one. In order to justify this statement we observe first that...

On Conformal Mapping of Nearly Circular Regions

X. Conformal Mapping

Innovations in conformal mapping continue to extend this classical technique to more complicated configurations, and surveys of the various techniques available are given in Ref. [7] and Ref. [1]. Some specific recommendations of techniques and tools are given in Ref. [7]. Conformal systems have advantage the of introducing the fewest additional terms in transformed partial differential equatio...

Conformal Mapping and Ellipses

We answer a question raised by M. Chuaqui, P. Duren, and B. Osgood by showing that a conformal mapping of a simply connected domain cannot take two circles onto two proper ellipses. The goal of this note is to prove the following. Proposition 1. Let Ω be a simply connected domain on C = C ∪ {∞} containing circles (on C) C1 and C2, C1 = C2. Let f be a conformal mapping from Ω into C. If f maps e...