• Corpus ID: 231698356

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… 
View PDF on arXiv
4 Citations
Methods Citations
1

4 Citations

De Rham algebras of closed quasiregularly elliptic manifolds are Euclidean

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

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

. 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

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

13 References

A bound on the cohomology of quasiregularly elliptic manifolds

We show that a closed, connected and orientable Riemannian manifold of dimension $d$ that admits a quasiregular mapping from $\mathbb R^d$ must have bounded cohomological dimension independent of the…

Mappings of Bounded Mean Distortion and Cohomology

We obtain a quantitative cohomological boundedness theorem for closed manifolds receiving entire mappings of bounded mean distortion and finite lower order. We also prove an equidistribution theorem…

Remarks On and Around Bounded Differential Forms

Various exotic cohomology groups can be defined by imposing boundedness conditions on cochains. This note discusses what happens if we impose boundedness conditions in the standard deRham complex of…

Integral estimates for null Lagrangians

Sobolev spaces of differential forms are studied, Lp-projections onto exact forms are introduced as a tool to obtain integral estimates for null Lagrangians. New results on compensated compactness…

Measure theory and fine properties of functions

GENERAL MEASURE THEORY Measures and Measurable Functions Lusin's and Egoroff's Theorems Integrals and Limit Theorems Product Measures, Fubini's Theorem, Lebesgue Measure Covering Theorems…

Real And Abstract Analysis

The first € price and the £ and $ price are net prices, subject to local VAT, and the €(D) includes 7% for Germany, the€(A) includes 10% for Austria.

Quasiregular curves: Hölder continuity and higher integrability

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

Averages of the counting function of a quasiregular mapping

Analytical foundations of the theory of quasiconformal mappings in R^n

Quasiregular mappings

  • Ergebnisse der Mathematik und ihrer Grenzgebiete