Small eigenvalues of random 3-manifolds

Hamenstädt, Ursula; Viaggi, Gabriele

doi:10.1090/tran/8564

Small eigenvalues of random 3-manifolds
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by Ursula Hamenstädt and Gabriele Viaggi PDF

Trans. Amer. Math. Soc. 375 (2022), 3795-3840 Request permission

Abstract:

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

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