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On the Ends of Trajectories

In: Differential Geometry and Complex Analysis

Author

Listed:
  • Albert Marden
  • Kurt Strebel

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.

Suggested Citation

  • Albert Marden & Kurt Strebel, 1985. "On the Ends of Trajectories," Springer Books, in: Isaac Chavel & Hershel M. Farkas (ed.), Differential Geometry and Complex Analysis, pages 195-204, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-69828-6_14
    DOI: 10.1007/978-3-642-69828-6_14
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