On a Vӓisӓlӓ-type inequality for the angular dilatation of mappings and some of its applications

Abstract

For a subtype of mappings with finite distortion f : D → D′, D, D′ ⊂ ℝⁿ; n ≥ 2; which admit the existence of branch points, a modular inequality playing an essential role in the study of various problems of planar and spatial mappings is established. As an application, the problem of removal of isolated singularities of open discrete mappings with finite length distortion is investigated.