Variation of quasiconformal mappings on lines
Volume 195 / 2009
Studia Mathematica 195 (2009), 257-274
MSC: Primary 30C62; Secondary 26A45, 30C65, 26B30.
DOI: 10.4064/sm195-3-5
Abstract
We obtain improved regularity of homeomorphic solutions of the reduced Beltrami equation, as compared to the standard Beltrami equation. Such an improvement is not possible in terms of Hölder or Sobolev regularity; instead, our results concern the generalized variation of restrictions to lines. Specifically, we prove that the restriction to any line segment has finite $p$-variation for all $p>1$ but not necessarily for $p=1$.
