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.Comment: 46 pages, 23 figures. Some minor corrections in v2, and a
clarification added in section 1
