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arXiv · 1407.2975

Everything is illuminated

Samuel Lelievre·Thierry Monteil·Barak Weiss
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Abstract

We study geometrical properties of translation surfaces: the finite blocking property, bounded blocking property, and illumination properties. These are elementary properties which can be fruitfully studied using the dynamical behavior of the SL(2,R)-action on the moduli space of translation surfaces. We characterize surfaces with the finite blocking property and bounded blocking property, completing work of the second-named author. Concerning the illumination problem, we also extend results of Hubert-Schmoll-Troubetzkoy, removing the hypothesis that the surface in question is a lattice surface, thus settling a conjecture. Our results crucially rely on the recent breakthrough results of Eskin-Mirzakhani and Eskin-Mirzakhani-Mohammadi, and on related results of Wright.

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Samuel Lelievre, Thierry Monteil, Barak Weiss. 2014-07-10. Everything is illuminated. https://doi.org/10.2140/gt.2016.20.1737

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