On the local and boundary behaviour of mappings of factor spaces

Abstract

In this article, we study mappings acting between domains of two factor spaces by certain groups of Möbius automorphisms of the unit ball that act discontinuously and do not have fixed points. For such mappings, we have established estimates for the distortion of the modulus of families of paths, which are similar to the well-known Poletsky and Väisälä inequalities. As applications, we have obtained several important results on the local and boundary behaviour of mappings.

Keywords:

• Mappings
• finite and bounded distortion
• factor spaces
• local and boundary behaviour

AMS SUBJECT CLASSIFICATIONS:

• Primary 30C65
• Secondary 32U20
• 31B15

Disclosure statement

No potential conflict of interest was reported by the author(s).