@inbook{57a3bbfb378a44779b83917f9b6ddce5,
title = "Some intrinsic constructions on compact Riemann surfaces",
abstract = "For any prescribed differential principal part on a compact Riemann surface, there are uniquely determined and intrinsically defined meromorphic abelian differentials with these principal parts, defined independently of any choice of a marking of the surface or of a basis for the holomorphic abelian differentials, and they are holomorphic functions of the singularities. They can be constructed explicitly in terms of intrinsically defined cross-ratio functions on the Riemann surfaces, the classical cross-ratio function for the Riemann sphere, and natural generalizations for surfaces of higher genus.",
keywords = "Abelian differentials, Cross-ratio function, Riemann surfaces",
author = "Gunning, {Robert C.}",
year = "2013",
doi = "10.1007/978-1-4614-4075-8_13",
language = "English (US)",
isbn = "9781461440741",
series = "Developments in Mathematics",
pages = "303--324",
editor = "Hershel Farkas and Marvin Knopp and Robert Gunning and B.A Taylor",
booktitle = "From Fourier Analysis and Number Theory to Radon Transforms and Geometry",
}