Quasiconformal mappings and singularity of boundary distortion |
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Authors: | Tomi Nieminen Ignacio Uriarte-Tuero |
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Affiliation: | 1.Department of Mathematics and Statistics,University of Jyv?skyl?,Jyv?skyl?,Finland;2.Mathematics Department,University of Missouri,Columbia,USA;3.Fields Institute,Toronto,Canada |
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Abstract: | We extend a well-known theorem of Jones and Makarov [8] on the singularity of boundary distortion of planar conformal mappings. Using a different technique, we recover the previous result and generalize the result to quasiconformal mappings of the unit ball ⊂_∝ n , n ≥ 2. We also establish an estimate on the Hausdorff (gauge) dimension of the boundary of the image domain outside an exceptional set of given size on the sphere ∂ and show that this estimate is essentially sharp. |
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