# Signed quasiregular curves

@inproceedings{Heikkila2021SignedQC, title={Signed quasiregular curves}, author={Susanna Heikkila}, year={2021} }

Abstract. We define a subclass of quasiregular curves, called signed quasiregular curves, which contains holomorphic curves and quasiregular mappings. As our main result, we prove a growth theorem of BonkHeinonen type for signed quasiregular curves. To obtain our main result, we prove that signed quasiregular curves satisfy a weak reverse Hölder inequality and that this weak reverse Hölder inequality implies the main result. We also obtain higher integrability for signed quasiregular curves…

## 4 Citations

### De Rham algebras of closed quasiregularly elliptic manifolds are Euclidean

- Mathematics
- 2023

We show that, if a closed, connected, and oriented Riemannian $n$-manifold $N$ admits a non-constant quasiregular mapping from the Euclidean $n$-space $\mathbb R^n$, then the de Rham cohomology…

### Pushforward of currents under Sobolev maps

- Mathematics
- 2023

We prove that a Sobolev map from a Riemannian manifold into a complete metric space pushes forward almost every compactly supported integral current to an Ambrosio--Kirchheim integral current in the…

### Finite distortion curves: Continuity, Differentiability and Lusin's (N) property

- Mathematics
- 2022

. We deﬁne ﬁnite distortion ω -curves and we show that for some forms ω and when the distortion function is suﬃciently exponentially integrable the map is continuous, diﬀerentiable almost everywhere…

### Quasiregular Curves of Small Distortion in Product Manifolds

- Materials ScienceThe Journal of Geometric Analysis
- 2022

We consider, for n⩾3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…

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### Quasiregular curves: Hölder continuity and higher integrability

- MathematicsComplex Analysis and its Synergies
- 2021

We show that a K-quasiregular ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

### Quasiregular mappings

- Ergebnisse der Mathematik und ihrer Grenzgebiete