Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 305-347

MEROMORPHIC QUADRATIC DIFFERENTIALS WITH HALF-PLANE STRUCTURES

Subhojoy Gupta

Aarhus University, Center for Quantum Geometry of Moduli Spaces
Ny Munkegade 118, DK 8000 Aarhus C, Denmark; sgupta 'at' qgm.au.dk

Abstract. We prove the existence of "half-plane differentials" with prescribed local data on any Riemann surface. These are meromorphic quadratic differentials with higher-order poles which have an associated singular flat metric isometric to a collection of euclidean half-planes glued by an interval-exchange map on their boundaries. The local data is associated with the poles and consists of the integer order, a non-negative real residue, and a positive real leading order term. This generalizes a result of Strebel for differentials with double-order poles, and associates metric spines with the Riemann surface.

2010 Mathematics Subject Classification: Primary 30F30, 30F60.

Key words: Quadratic differentials, quasiconformal maps, flat surfaces.

Reference to this article: S. Gupta: Meromorphic quadratic differentials with half-plane structures. Ann. Acad. Sci. Fenn. Math. 39 (2014), 305-347.

Full document as PDF file

doi:10.5186/aasfm.2014.3908