On the Ends of Trajectories

Albert Marden and Kurt Strebel

A chapter in Differential Geometry and Complex Analysis, 1985, pp 195-204 from Springer

Abstract: Abstract The purpose of this note is to establish a certain basic property concerning in particular the “ends” of the trajectories and more generally of the geodesics of a (holomorphic) quadratic differential φ d z 2 of finite norm $$\left\| \varphi \right\| = \int {\int {\left| \varphi \right|dxdy} }$$ on an arbitrary Riemann surface R. In the remainder of this section we will briefly recall certain aspects of the geometry associated with these differentials. The theorem is stated in Sect. 2.

Keywords: Riemann Surface; Homotopy Class; Quadratic Differential; Geodesic Lamination; Free Homotopy Class (search for similar items in EconPapers)
Date: 1985
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DOI: 10.1007/978-3-642-69828-6_14

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