Abstract.
We prove that a for a mapping f of finite distortion \(K\in L^{p/(n-p)}\), the \((n-p)\)-Hausdorff measure of any point preimage is zero provided \(J_f\) is integrable, \(Df\in L^s\) with \(s>p\), and the multiplicity function of f is essentially bounded. As a consequence for \(p=n-1\) we obtain that the mapping is then open and discrete.
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Received: 18 June 2001 / Revised version: 31 January 2002 / Published online: 27 June 2002
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Hencl, S., Malý, J. Mappings of finite distortion: Hausdorff measure of zero sets. Math Ann 324, 451–464 (2002). https://doi.org/10.1007/s00208-002-0347-z
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DOI: https://doi.org/10.1007/s00208-002-0347-z