On Mirzakhani's twist torus conjecture
Geometric Topology
2025-10-16 v3 Dynamical Systems
Abstract
We address 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. We also identify a number of other expanding families of twist tori whose limiting distributions are mutually singular to Lebesgue.
Keywords
Cite
@article{arxiv.2405.12106,
title = {On Mirzakhani's twist torus conjecture},
author = {Aaron Calderon and James Farre},
journal= {arXiv preprint arXiv:2405.12106},
year = {2025}
}
Comments
The final section of the paper was rewritten in order to incorporate referee's suggestions and fine-tune the exposition. Final version, to appear in Duke