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arxiv: 1301.0332 · v2 · pith:PTB2I2RGnew · submitted 2013-01-02 · 🧮 math.GT · math.CV

Meromorphic quadratic differentials with half-plane structures

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keywords differentialspolesassociateddatahalf-planelocalmeromorphicmetric
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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.

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