Quasi-symmetric mappings and their generalizations on Riemannian manifolds

A relation between η-quasi-symmetric homomorphisms and K -quasiconformal mappings on n -dimensional smooth connected Riemannian manifolds has been studied. The main results of the research are presented in Theorems 2.6 and 2.7. Several conditions for the boundary behavior of η-quasi-symmetric homomorphisms between two arbitrary domains with weakly flat boundaries and compact closures, QED and uniform domains on the Riemannian manifolds, which satisfy the obtained results, were also formulated. In addition, quasiballs, c -locally connected domains, and the corresponding results were also considered.