Boundary behaviour of open, light mappings in metric measure spaces

Abstract

We study the boundary behaviour of open, light mappings satisfying generalized modular inequalities in general metric measure spaces. We extend in this way known facts from the theory of quasiregular mappings and from their recent generalizations, namely the mappings of finite distortion and the so called ring mappings.

On the radial limits of mappings on Riemannian manifolds

“…Let Γ ∈ A(D) and ∆ = {γ ∈ Γ|γ is rectifiable and f • γ 0 is absolutely continuous} and using Fuglede's theorem from [11], Theorem 2.1, we see that…”

“…The classes of mappings distinguished by moduli inequalities were intensively studied in the last 20 years. Such an approach was proposed by Martio, first on mappings between open sets in R n in [2][3], [6][7], [9][10], [37][38][39], [47][48], [52][53] and then on metric measure spaces in [11][12], [25][26], [49][50], [54][55]. For some weight ω and some p, q > 1 a Poletsky generalized modular inequality of type…”