On Makarov’s Principle in Conformal Mapping

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...

Breakthrough in Conformal Mapping

Few analytical techniques are better known to students of applied mathematics than conformal mapping. It is the classical method for solving problems in continuum mechanics, electrostatics, and other fields involving the two-dimensional Laplace and Poisson equations. To employ the method, one needs an explicit mapping function from some standard domain— such as the unit disk or upper half plane...

On Conformal Mapping of Nearly Circular Regions

Conformal Mapping in Linear Time

Given any ǫ > 0 and any planar region Ω bounded by a simple n-gon P we construct a (1 + ǫ)-quasiconformal map between Ω and the unit disk in time C(ǫ)n. One can take C(ǫ) = C + C log 1 ǫ log log 1 ǫ . Date: August 13, 2009. 1991 Mathematics Subject Classification. Primary: 30C35, Secondary: 30C85, 30C62 .