Hopf Differentials and Smoothing Sobolev Homeomorphisms
نویسندگان
چکیده
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.
منابع مشابه
Planar Sobolev Homeomorphisms and Hausdorff Dimension Distortion
We investigate how planar Sobolev-Orlicz homeomorphisms map sets of Hausdorff dimension less than two. With the correct gauge functions the generalized Hausdorff measures of the image sets are shown to be zero.
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