Hopf differentials and smoothing Sobolev homeomorphisms
classification
🧮 math.CV
keywords
homeomorphismshopfplanarsobolevalgebraapplicationapproximateddiffeomorphisms
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We prove that planar homeomorphisms can be approximated by diffeomorphisms in the Sobolev space $W^{1,2}$ and in the Royden algebra. As an application, we show that every discrete and open planar mapping with a holomorphic Hopf differential is harmonic.
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