Liouville-type theorems for conformal mappings and their application

In the present paper we prove Liouville-type theorems: non-existence theorems for conformal mappings of complete Riemannian manifolds. In addition, we give an application of these results to the theory of conharmonic transformations. A part of these results was announced in our reports on the conferences "Differential Geometry and its Applications" (July 11-15, 2016, Brno, Czech Republic) and "International Conference on Algebra, Analysis and Geometry" (June 26-July 2, 2016, Kazan, Russia).