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Conformal Fitness and Uniformization of Holomorphically Moving Disks
Let be a family of topological disks on the
Riemann sphere containing the origin 0 whose boundaries undergo a holomorphic
motion over the unit disk . We study the question of when there
exists a family of Riemann maps which depends
holomorphically on the parameter . We give five equivalent conditions which
provide analytic, dynamical and measure-theoretic characterizations for the
existence of the family , and explore the
consequences.Comment: 32 pages, 4 figure
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