On tube-log Riemann surfaces and primitives of rational functions

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.

References in corpus (1)

• Log-Riemann Surfaces

Cited by in corpus (2)

• The Cantor Riemannium
• The Ramificant Determinant