Topological Properties of Mappings with Finite Distortion on Carnot Groups
摘要
We prove thatevery mapping with finite distortion on a Carnot groupis open and discrete provided that it is quasilight and the distortion coefficient is integrable.Also, we estimate the Hausdorff dimension of the preimages of pointsfor mappings on a Carnot groupwith a bounded multiplicity functionand summable distortion coefficient.Furthermore, we give some example showing thatthe obtained estimates cannot be improved.