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Circle Domain

A circle domain is a nonempty connected open subset of the Riemann sphere whose complementary components are closed round disks or single points. The definition allows infinitely many components.

Conformal equivalence means a bijective conformal mapping with conformal inverse.

A circle domain is conformally rigid if every conformal equivalence onto another circle domain is the restriction of a Möbius transformation.

See also

Conformal Mapping, Conformally Removable Set, He-Schramm Conjecture, Moebius Transformation, Riemann Sphere

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References

Ntalampekos, D. and Younsi, M. "Rigidity Theorems for Circle Domains." Invent. Math. 220, 129-183, 2020. https://doi.org/10.1007/s00222-019-00921-1.

Cite this as:

Weisstein, Eric W. "Circle Domain." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CircleDomain.html

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