TY - CHAP

T1 - Some intrinsic constructions on compact Riemann surfaces

AU - Gunning, Robert Clifford

PY - 2013/9/2

Y1 - 2013/9/2

N2 - 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.

AB - 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.

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U2 - 10.1007/978-1-4614-4075-8_13

DO - 10.1007/978-1-4614-4075-8_13

M3 - Chapter

AN - SCOPUS:84883063640

SN - 9781461440741

T3 - Developments in Mathematics

SP - 303

EP - 324

BT - From Fourier Analysis and Number Theory to Radon Transforms and Geometry

A2 - Farkas, Hershel

A2 - Knopp, Marvin

A2 - Gunning, Robert

A2 - Taylor, B.A

ER -