The conformal radius is a concept from complex analysis and geometric function theory, particularly in the study of conformal mappings. It provides a measure of the "size" of a domain in a way that is invariant under conformal (angle-preserving) transformations.
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For a simply connected domain and , the conformal radius is , where maps the unit disc conformally onto with . Disc automorphisms fixing zero are rotations, so the value is independent of the chosen map.