2021/01/25 by Heikkilä, Susanna · 1 citation
#53C15 #53C57 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Primary 30C65 #Secondary 32A30 #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2101.09943
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 Hölder inequality and that this weak reverse Hölder 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.