English

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.

Keywords

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

R2 v1 2026-06-21T23:03:08.113Z