Variation of quasiconformal mappings on lines

Details Variation of quasiconformal mappings on lines Variation of quasiconformal mappings on lines

2009-01-10

arxiv.org/abs/0901.1400v1

Studia Math. 195 (2009), no.3, 257-274.

Mathematics

Complex Variables

18 pages, 1 figure, 2 open questions

Scientific paper

10.4064/sm195-3-5

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 Holder 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.

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