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arXiv · 1805.02906

Controlled diffeomorphic extension of homeomorphisms

Pekka Koskela·Zhuang Wang·Haiqing Xu
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Abstract

Let $\Omega$ be an internal chord-arc Jordan domain and $\varphi:\mathbb S\rightarrow\partial\Omega$ be a homeomorphism. We show that $\varphi$ has finite dyadic energy if and only if $\varphi$ has a diffeomorphic extension $h: \mathbb D\rightarrow \Omega$ which has finite energy.

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Pekka Koskela, Zhuang Wang, Haiqing Xu. 2018-05-08. Controlled diffeomorphic extension of homeomorphisms. https://doi.org/10.1016/j.na.2018.04.020

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