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arXiv · 1412.4046

Manifolds of quasiconformal mappings and the nonlinear Beltrami equation

Kari Astala·Albert Clop·Daniel Faraco·Jarmo Jääskeläinen
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Abstract

In this paper we show that the homeomorphic solutions to each nonlinear Beltrami equation $\partial_{\bar{z}} f = \mathcal{H}(z, \partial_{z} f)$ generate a two-dimensional manifold of quasiconformal mappings $\mathcal{F}_{\mathcal{H}} \subset W^{1,2}_{\mathrm{loc}}(\mathbb{C})$. Moreover, we show that under regularity assumptions on $\mathcal{H}$, the manifold $\mathcal{F}_{\mathcal{H}}$ defines the structure function $\mathcal{H}$ uniquely.

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Kari Astala, Albert Clop, Daniel Faraco, Jarmo Jääskeläinen. 2014-12-12. Manifolds of quasiconformal mappings and the nonlinear Beltrami equation. https://doi.org/10.1007/s11854-019-0059-x

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