Everything Is Illuminated
نویسندگان
چکیده
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 [Mon05]. Concerning the illumination problem, we also extend results of Hubert-Schmoll-Troubetzkoy [HST08], removing the hypothesis that the surface in question is a lattice surface, thus settling a conjecture of [HST08]. Our results crucially rely on the recent breakthrough results of Eskin-Mirzakhani [EM] and Eskin-Mirzakhani-Mohammadi [EMM], and on related results of Wright [Wria].
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