@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",

}