Hopf differentials and smoothing Sobolev homeomorphisms

T. Iwaniec, L.V. Kovalev, J. Onninen

Abstract: 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.

Journal: Int Math Res Notices (2012) 2012 (14): 3256-3277.

DOI: 10.1093/imrn/rnr144