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arXiv · 1412.4248

Estimates for the dilatation of $\sigma$-harmonic mappings

Giovanni Alessandrini·Vincenzo Nesi
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Abstract

We consider planar $\sigma$-harmonic mappings, that is mappings $U$ whose components $u^1$ and $u^2$ solve a divergence structure elliptic equation ${\rm div} (\sigma \nabla u^i)=0$, for $i=1,2$. We investigate whether a locally invertible $ \sigma$-harmonic mapping $U$ is also quasiconformal. Under mild regularity assumptions, only involving $\det \sigma$ and the antisymmetric part of $\sigma$, we prove quantitative bounds which imply quasiconformality.

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Giovanni Alessandrini, Vincenzo Nesi. 2014-12-13. Estimates for the dilatation of $\sigma$-harmonic mappings. https://arxiv.org/abs/1412.4248

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