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 Length: Definition 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

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### Famous quotes containing the word length:

“When one man has reduced a fact of the imagination to be a fact to his understanding, I foresee that all men will at *length* establish their lives on that basis.”

—Henry David Thoreau (1817–1862)