Liouville-type theorems for conformal mappings and their application

TL;DR

This paper establishes Liouville-type theorems that prevent certain conformal mappings on complete Riemannian manifolds and applies these results to conharmonic transformations, advancing understanding in differential geometry.

Contribution

It proves new non-existence theorems for conformal mappings on complete Riemannian manifolds and applies these to the study of conharmonic transformations.

Findings

Proved Liouville-type non-existence theorems for conformal mappings.

Applied these theorems to conharmonic transformations.

Extended previous results announced at international conferences.

Abstract

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).