Extremal Length

In the mathematical theory of conformal and quasiconformal mappings, the extremal length of a collection of curves is a conformal invariant of . More specifically, suppose that is an open set in the complex plane and is a collection of paths in and is a conformal mapping. Then the extremal length of is equal to the extremal length of the image of under . 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.

Read more about Extremal LengthDefinition of Extremal Length, Examples, Elementary Properties of Extremal Length, Conformal Invariance of Extremal Length, Some Applications of Extremal Length, Extremal Length in Higher Dimensions, Discrete Extremal Length

Other articles related to "length, extremal length":

Quasiconformal Mapping - Definition
... eigenvalues represent, respectively, the squared length of the major and minor axis of the ellipse obtained by pulling back along f the unit circle in the tangent plane ... A definition based on the notion of extremal length is as follows ... If there is a finite K such that for every collection Γ of curves in D the extremal length of Γ is at most K times the extremal length of { ƒ o γ γ ∈ Γ } ...
Discrete Extremal Length
... There are two variants of extremal length in this setting ... To define the edge extremal length, originally introduced by R ... The -length of a path is defined as the sum of over all edges in the path, counted with multiplicity ...

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