About mappings with modulus conditions in metric spaces - Afanas'eva, O.S. (Reports of the National Academy of Sciences of Ukraine, 2014)
The properties of continually weakly flat spaces that are a generalization of the recently introduced Loewner spaces including the well-known Carnot and Heisenberg groups are studied. The theory of the boundary behaviors of continually ring Q-homeomorphisms relative to a p-module between continual domains in metric spaces with measures is developed. In particular, the consequences for the case of continually weakly flat spaces and continual quasiextremal length domains by Gehring–Martio are presented.