|
|||||
|
|
|
|
|
|
|
|
|
Everything is
illuminated
Samuel Lelièvre, Thierry Monteil and Barak Weiss |
|
Geometry & Topology 20 (2016) 1737–1762
|
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. |
Keywords
illumination, translation surfaces, billiards, everything
|
Mathematical Subject Classification 2010
Primary: 37E35
Secondary: 53A99
|
References |
Publication
Received: 4 February 2015
Revised: 2 June 2015
Accepted: 16 July 2015
Published: 4 July 2016
Proposed: Jean-Pierre Otal
Seconded: Ian Agol, Bruce Kleiner
|
Authors |
| Samuel Lelièvre | |
| Laboratoire de mathématique
d’Orsay UMR 8628 CNRS Université Paris-Sud 11 Bâtiment 425, campus Orsay-vallée 91405 Orsay Cedex France |
|
| Thierry Monteil | |
| Laboratoire d’Informatique de Paris
Nord UMR 7030 CNRS Université Paris 13 F-93430 Villetaneuse France |
|
| Barak Weiss | |
| School of Mathematical
Sciences Tel Aviv University Tel Aviv 69978 Israel |
|
|
