On Mirzakhani's twist torus conjecture

Aaron Calderon; James Farre

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arXiv · 2405.12106

On Mirzakhani's twist torus conjecture

Aaron Calderon·James Farre

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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.

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Aaron Calderon, James Farre. 2024-05-20. On Mirzakhani's twist torus conjecture. https://arxiv.org/abs/2405.12106

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