Mappings of finite distortion: Hausdorff measure of zero sets |
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| Authors: | Stanislav Hencl Jan Malý |
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| Affiliation: | (1) Charles University, Department KMA of the Faculty of Mathematics and Physics, Sokolovská 83, CZ-18675 Praha 8, Czech Republic (e-mail: {hencl,maly}@karlin.mff.cuni.cz) , CZ |
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| Abstract: | We prove that a for a mapping f of finite distortion , the -Hausdorff measure of any point preimage is zero provided is integrable, with , and the multiplicity function of f is essentially bounded. As a consequence for we obtain that the mapping is then open and discrete. Received: 18 June 2001 / Revised version: 31 January 2002 / Published online: 27 June 2002 |
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| Keywords: | Mathematics Subject Classification (2000): 30C65 26B10 74B20 |
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