On isolated singularities of mappings with finite length distortion

Abstract

Here we give a survey of various integral criteria in terms of inner dilatations $K_{I}$ for the removability of isolated singularities of mappings with finite length distortion in $\mathbb{R}^{n}$, $n\geq 2$, that are a natural extension of the well-known Martio-Vaisal a mappings with bounded length distortion. In particular, the survey includes many effective integral criteria of the types of BMO, bounded mean oscillation by John-Nirenberg, FMO, finite mean oscillation, Calderon-Zygmund, Lehto, and Orlicz.