Quasiconformal geometry and removable sets for conformal mappings
Abstract
We study metric spaces defined via a conformal weight, or more generally a measurable Finsler structure, on a domain $\Omega \subset \mathbb{R}^2$ that vanishes on a compact set $E \subset \Omega$ and satisfies mild assumptions. Our main question is to determine when such a space is quasiconformally equivalent to a planar domain. We give a characterization in terms of the notion of planar sets that are removable for conformal mappings. We also study the question of when a quasiconformal mapping can be factored as a 1quasiconformal mapping precomposed with a biLipschitz map.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 DOI:
 10.48550/arXiv.2006.02776
 arXiv:
 arXiv:2006.02776
 Bibcode:
 2020arXiv200602776I
 Keywords:

 Mathematics  Metric Geometry;
 Primary 30L10. Secondary 30C35;
 52A38;
 53B40
 EPrint:
 48 pages, 2 figures. Fixed LaTeX compiling error