Mappings of finite distortion: Hausdorff measure of zero sets

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.