Mappings of finite distortion: Hausdorff measure of zero sets

摘要

We prove that a for a mapping f of finite distortion $Kin L^{p/(n-p)}$ , the $(n-p)$ -Hausdorff measure of any point preimage is zero provided $J_f$ is integrable, $Dfin L^s$ 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.