ON MIRZAKHANI’S TWIST TORUS CONJECTURE
Abstract
This article addresses a conjecture of Mirzakhani about the statistical behavior of certain expanding families of “twist tori” in the moduli space of hyperbolic surfaces, showing that they equidistribute to a certain Lebesgue-class measure along almost all sequences. It also identifies a number of other expanding families of twist tori whose limiting distributions are mutually singular to Lebesgue.
Fields of Study & Subjects
Mathematics and Applications
Mathematical Dynamics and Fractals
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Duke Mathematical Journal
- Publisher
- Duke University Press
- Volume
- 175
- Issue
- 11
- Pages
- 2081–2124
- Publication date
- 15 August 2026
- Language
- EN