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The area of the complement of a conformally rigid domain


Author: Marius Overholt
Journal: Proc. Amer. Math. Soc. 103 (1988), 448-450
MSC: Primary 30C55
DOI: https://doi.org/10.1090/S0002-9939-1988-0943064-3
MathSciNet review: 943064
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Abstract: A hyperbolic subdomain $ D$ of $ {\mathbf{\hat C}}$ is said to be (conformally) rigid if any conformal map from $ D$ into $ {\mathbf{\hat C}}$ is either a Möbius transformation, or has Schwarzian norm larger than a positive constant depending on $ D$ only. We show that the complement of a conformally rigid domain has zero area.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0943064-3
Keywords: Conformal map, Schwarzian derivative, rigid domain
Article copyright: © Copyright 1988 American Mathematical Society

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