Hopf Differentials and Smoothing Sobolev Homeomorphisms

By Tadeusz Iwaniec, L. Kovalev, Jani Onninen. 2010

61 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/00cf71d5c7a6aae38631fe77098295c506026311

How researchers see this paper

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In Geometry and Topology

1. Jani Onninen
2. Tadeusz Iwaniec
3. L. Kovalev
4. Ngin-Tee Koh
5. Sara Daneri
6. Aldo Pratelli
7. Pekka Koskela
8. S. Hencl

In Mathematical Physics

1. Sara Daneri
2. Jani Onninen
3. Aldo Pratelli

In Statistical and Nonlinear Physics

1. Sara Daneri
2. Jani Onninen
3. Dachun Yang

Citations in the corpus

• Existence of energy-minimal diffeomorphisms between doubly connected domains (2010, background): “By virtue of the density of diffeomorphisms in H 1,2 (�, � ∗ ) ,s ee [ 20 ], the”
• Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms (2011, background): “Recently, Iwaniec, Kovalev and Onninen [22] almost completely solved the approximation problem of planar Sobolev homeomorphisms, proving that whenever u belongs to W 1,p for some 1 < p < +∞, then it can be approximated by smooth diffeomorphisms v in the W 1,p norm (improving the previous result for ”