Local homeomorphisms having local<b><i>ACL</i></b>^{<b><i>n</i></b>}inverses

Abstract

Abstract We consider local homeomorphisms between domains from R n satisfying condition (N) and having local ACL n inverses. For such mappings we generalize some basic facts from the theory of quasiregular mappings as the modular inequality of Poleckii and estimates of the modulus of spherical rings from [Koskela, P. and Onninen, J., 2002, Mappings of finite distortion: capacity and modulus inequalities, Preprint 257, University of Jyväskylä; Martio, O., Ryazanov, V., Srebro, U. and Yakubov, E., 2005, On Q-homeomorphisms, Annales Academiae Scientarum Fennicae Mathematica, 30, 49–69] and [Martio, O., Ryazanov, V., Srebro, U. and Yakubov, E., 2002, Mappings of finite length distortion, Preprint 322, Reports Mathematics Department, University of Helsinki], and we use these facts to extend Zoric's theorem and to calculate the radius of injectivity for this class of mappings. Keywords: Zoric's theoremEliminability results AMS Subject Classification: : 30C65 Acknowledgement This research is supported by the Romanian Ministry of Education and Research, CEEx Program, Project 2-CEx06-10/25.07.2006.