Quasiregular values from generalized manifold with controlled geometry

The main aim of this paper is to establish the Reshetnyak’s theorem for quasiregualr values from generalized $n$-manifold with suitable controlled geometry to Euclidean space ${\mathbb{R}}^n\mathrm{.}$ This generalizes a previous result due to Kangasniemi and Onninen on the setting of Euclidean space [A single-point Reshetnyak’s theorem, Trans. Amer. Math. Soc., 378(2025): 3105-3128].