Manifolds of quasiconformal mappings and the nonlinear Beltrami equation

Kari Astala,Albert Clop,Daniel Faraco,Jarmo Jääskeläinen

Journal d'Analyse Mathématique（2019）

引用 2|浏览13

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摘要

In this paper we show that the homeomorphic solutions to each nonlinear Beltrami equation ∂_z̅f=ℋ(z,∂_zf) generate a two-dimensional manifold of quasiconformal mappings ℱ_ℋ⊂W_loc^1,2(ℂ) . Moreover, we show that under regularity assumptions on ℋ , the manifold ℱ_ℋ defines the structure function ℋ uniquely.

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