Homeomorphisms between Finsler manifolds satisfying the Rohde condition

Abstract

We study the main features of homeomorphisms between two Finsler manifolds satisfying the Rohde condition, i.e. the difference between the moduli of geodesic rings in the image and its preimage is uniformly bounded from below and above. Some equivalent conditions for such a characterization are established. Also we investigate the absolute continuity and the relations to the class of mappings with finite are distortion. As applications, the boundary correspondence results for homeomorphisms satisfying the Rohde condition between regular domains are also presented.