extremal lengthとは 意味・読み方・使い方

In the mathematical theory of conformal and quasiconformal mappings, the extremal length of a collection of curves Γ is a conformal invariant of Γ. More specifically, suppose that D is an open set in the complex plane and Γ is a collection of paths in D and is a conformal mapping. Then the extremal length of Γ is equal to the extremal length of the image of Γ under f. For this reason, the extremal length is a useful tool in the study of conformal mappings. Extremal length can also be useful in dimensions greater than two, but the following deals primarily with the two dimensional setting.