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Evolution dynamics of conformal maps with quasiconformal extensions

Alexander Vasil'ev
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Abstract

We study one-parameter curves on the universal Teichmüller space $T$ and on the homogeneous space $M=\Diff S^1/\Rot S^1$ 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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Alexander Vasil'ev. 2004-10-08. Evolution dynamics of conformal maps with quasiconformal extensions. https://arxiv.org/abs/math/0410229

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