Evolution dynamics of conformal maps with quasiconformal extensions
Alexander Vasil'ev
Abstract
We study one-parameter curves on the universal Teichmüller space T and on the homogeneous space M= S1/ S1 embedded into T. As a result, we deduce evolution equations for conformal maps that admit quasiconformal extensions and, in particular, such that the associated quasidisks are bounded by smooth Jordan curves. Some applications to Hele-Shaw flows of viscous fluids are given.
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