Signed quasiregular curves

TL;DR

This paper introduces signed quasiregular curves, a new subclass encompassing holomorphic and quasiregular mappings, and establishes a growth theorem along with higher integrability and value distribution results for them.

Contribution

The paper defines signed quasiregular curves and proves a Bonk-Heinonen type growth theorem, along with weak reverse Hölder inequalities and cohomological value distribution results.

Findings

Signed quasiregular curves satisfy a weak reverse Hölder inequality.

Higher integrability properties are established for these curves.

A cohomological value distribution theorem is proved using the main growth result.

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 Bonk-Heinonen type for signed quasiregular curves. To obtain our main result, we prove that signed quasiregular curves satisfy a weak reverse H\"older inequality and that this weak reverse H\"older inequality implies the main result. We also obtain higher integrability for signed quasiregular curves. Further, we prove a cohomological value distribution result for signed quasiregular curves by using our main result and equidistribution.