Distortion of area and dimension under quasiconformal mappings in the plane.
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- Record sourced from PubMed, PMID 11607447.
- Also identified by PMC identifier 48104.
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Abstract
We find the exact estimates for the distortion of area and Hausdorff dimension under a K-quasiconformal mapping of the complex plane. This solves also the problem of finding the precise bound p(K) of the exponents p such that for each planar K-quasiconformal mapping f the Jacobian Jf is locally p-integrable; it follows that p(K) = 2K/(K - 1). Further consequences include among others the regularity and removability results for quasiregular mappings and sharp estimates for the complex Hilbert transform.