Capacity estimates, Liouville's theorem, and singularity removal for mappings with bounded \((p,q)\)-distortion
The boundary behavior of some subclass of mappings with finite distortion in Euclidean \(n\)-space is studied. For the so-called mappings with finite \((p, q)\)-distortion, some weighted capacity estimates are proved. As a consequence, analogues of the Liouville theorem are established. In particular, it is proved that the mappings mentioned above cannot omit sets of positive capacity. Moreover, theorems about removable isolated singularities are proved. In terms of mappings of finite \((p, q)\)-distortion, some classification of Riemann manifolds is given.
scientific article; zbMATH DE number 6526916
scientific article