arXiv math/04102292004-10-08math.APmath.CV

Evolution dynamics of conformal maps with quasiconformal extensions

Alexander Vasil'ev

备注：: 32 pages, 3 figures
发表信息：: Bull. Sci. Math. 129 (2005), no. 10, 831-859

英文摘要：

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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