Small eigenvalues of random 3-manifolds

Hamenstaedt, Ursula; Viaggi, Gabriele

doi:10.1090/tran/8564

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Small eigenvalues of random 3-manifolds

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Viaggi, Gabriele
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1090/tran/8564
(Publisher version)

https://doi.org/10.48550/arXiv.1903.08031
(Preprint)

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Citation

Hamenstaedt, U., & Viaggi, G. (2022). Small eigenvalues of random 3-manifolds. Transactions of the American Mathematical Society, 375(6), 3795-3840. doi:10.1090/tran/8564.

Cite as: https://hdl.handle.net/21.11116/0000-000A-75C6-3

Abstract

We show that for every $g\geq 2$ there exists a number $c(g)>0$ such that the
smallest positive eigenvalue of a random closed 3-manifold $M$ of Heegaard
genus $g$ is at most $c(g)/{\rm vol}(M)^2$.