Everything is illuminated

Samuel Lelièvre, Thierry Monteil, Barak Weiss

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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 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.

Original languageEnglish
Pages (from-to)1737-1762
Number of pages26
JournalGeometry and Topology
Volume20
Issue number3
DOIs
StatePublished - 4 Jul 2016
Externally publishedYes

Fingerprint

Dive into the research topics of 'Everything is illuminated'. Together they form a unique fingerprint.

Cite this