Geometry of periodic regions on flat surfaces and associated Siegel-Veech constants
| Autor: | Bauer, Max, Goujard, Elise |
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| Rok vydání: | 2014 |
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| Druh dokumentu: | Working Paper |
| Popis: | An Abelian differential gives rise to a flat structure (translation surface) on the underlying Riemann surface. In some directions the directional flow on the flat surface may contain a periodic region that is made up of maximal cylinders filled by parallel geodesics of the same length. The growth rate of the number of such regions counted with weights, as a function of the length, is quadratic with a coefficient, called Siegel-Veech constant, that is shared by almost all translation surfaces in the ambient stratum. We evaluate various Siegel-Veech constants associated to the geometry of configurations of periodic cylinders and their area, and study extremal properties of such configurations in a fixed stratum and in all strata of a fixed genus. Comment: 31 pages, 9 figures. The final publication is available at Springer via http://dx.doi.org/10.1007/s10711-014-0014-z |
| Databáze: | arXiv |
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