TY - JOUR
T1 - Everything is illuminated
AU - Lelièvre, Samuel
AU - Monteil, Thierry
AU - Weiss, Barak
N1 - Publisher Copyright:
© 2016, Mathematical Sciences Publishers. All rights reserved.
PY - 2016/7/4
Y1 - 2016/7/4
N2 - 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 and Troubetzkoy, removing the hypothesis that the surface in question is a lattice surface, thus settling a conjecture of theirs. Our results crucially rely on the recent breakthrough results of Eskin and Mirzakhani and of Eskin, Mirzakhani and Mohammadi, and on related results of Wright.
AB - 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 and Troubetzkoy, removing the hypothesis that the surface in question is a lattice surface, thus settling a conjecture of theirs. Our results crucially rely on the recent breakthrough results of Eskin and Mirzakhani and of Eskin, Mirzakhani and Mohammadi, and on related results of Wright.
UR - http://www.scopus.com/inward/record.url?scp=84978958331&partnerID=8YFLogxK
U2 - 10.2140/gt.2016.20.1737
DO - 10.2140/gt.2016.20.1737
M3 - Article
AN - SCOPUS:84978958331
SN - 1465-3060
VL - 20
SP - 1737
EP - 1762
JO - Geometry and Topology
JF - Geometry and Topology
IS - 3
ER -