Quasiregular values from generalized manifold with controlled geometry

TL;DR

This paper extends Reshetnyak's theorem to quasiregular values originating from generalized n-manifolds with controlled geometry, broadening the scope beyond Euclidean spaces.

Contribution

It generalizes Reshetnyak's theorem for quasiregular values from generalized n-manifolds with controlled geometry to Euclidean space.

Findings

Established Reshetnyak's theorem in a new geometric setting

Extended previous Euclidean results to generalized manifolds

Provided new tools for analyzing quasiregular mappings from complex manifolds

Abstract

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 $\mathbb{R}^{n}.$ 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].