On tube-log Riemann surfaces and primitives of rational functions
Complex Variables
2015-12-15 v1
Abstract
For a generic class of rational functions, we give an explicit description of the flat structure on the Riemann sphere induced by a meromorphic 1-form R(z)dz, where R is a rational function. The rational functions in the generic class we consider have only simple poles. We show that the flat structure may be obtained by pasting isometrically flat half-cylinders to a 'log-polygon', which is a domain bounded by straight line segments in a simply connected finite sheeted branched cover of C.
Cite
@article{arxiv.1512.04035,
title = {On tube-log Riemann surfaces and primitives of rational functions},
author = {Kingshook Biswas and Ricardo Perez-Marco},
journal= {arXiv preprint arXiv:1512.04035},
year = {2015}
}