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arXiv · 0901.1400

Variation of quasiconformal mappings on lines

Leonid V. Kovalev·Jani Onninen
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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 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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Leonid V. Kovalev, Jani Onninen. 2009-01-10. Variation of quasiconformal mappings on lines. https://doi.org/10.4064/sm195-3-5

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