Evolution dynamics of conformal maps with quasiconformal extensions

Details Evolution dynamics of conformal maps with quasiconformal extensions Evolution dynamics of conformal maps with quasiconformal extensions

2004-10-08

arxiv.org/abs/math/0410229v1

Bull. Sci. Math. 129 (2005), no. 10, 831-859

Mathematics

Analysis of PDEs

32 pages, 3 figures

Scientific paper

We study one-parameter curves on the universal Teichm\"uller 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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