Meromorphic quadratic differentials with half-plane structures
Geometric Topology
2013-02-26 v2 Complex Variables
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.
Cite
@article{arxiv.1301.0332,
title = {Meromorphic quadratic differentials with half-plane structures},
author = {Subhojoy Gupta},
journal= {arXiv preprint arXiv:1301.0332},
year = {2013}
}
Comments
46 pages, 23 figures. Some minor corrections in v2, and a clarification added in section 10