Geometry & Topology
- Geom. Topol.
- Volume 20, Number 3 (2016), 1737-1762.
Everything is illuminated
Samuel Lelièvre, Thierry Monteil, and Barak Weiss
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 –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.
Article information
Source
Geom. Topol., Volume 20, Number 3 (2016), 1737-1762.
Dates
Received: 4 February 2015
Revised: 2 June 2015
Accepted: 16 July 2015
First available in Project Euclid: 16 November 2017
Permanent link to this document
https://projecteuclid.org/euclid.gt/1510859001
Digital Object Identifier
doi:10.2140/gt.2016.20.1737
Mathematical Reviews number (MathSciNet)
MR3523067
Zentralblatt MATH identifier
06624257
Subjects
Primary: 37E35: Flows on surfaces
Secondary: 53A99: None of the above, but in this section
Keywords
illumination translation surfaces billiards everything
Citation
Lelièvre, Samuel; Monteil, Thierry; Weiss, Barak. Everything is illuminated. Geom. Topol. 20 (2016), no. 3, 1737--1762. doi:10.2140/gt.2016.20.1737. https://projecteuclid.org/euclid.gt/1510859001