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Moduli spaces of abelian differentials : the principal boundary, counting problems, and the Siegel-Veech constants

Alex Eskin, Howard Masur, Anton Zorich (2003)

Publications Mathématiques de l'IHÉS

A holomorphic 1-form on a compact Riemann surface S naturally defines a flat metric on S with cone-type singularities. We present the following surprising phenomenon: having found a geodesic segment (saddle connection) joining a pair of conical points one can find with a nonzero probability another saddle connection on S having the same direction and the same length as the initial one. A similar phenomenon is valid for the families of parallel closed geodesics. We give a complete description of...

New trends in geometric function theory.

Bulboacă, Teodor (ed.), Aouf, Mohamed K. (ed.), Cho, Nak Eun (ed.), Kanas, Stanisława R. (ed.), Obradovic, Milutin (ed.) (2010)

International Journal of Mathematics and Mathematical Sciences

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