Small eigenvalues of random 3-manifolds

2019/03/19 by Ursula Hamenstaedt, Hamenstaedt, Ursula, Gabriele Viaggi +1
Mathematics · #20P05 #30F60 #58C40 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1903.08031

openalex publication_date 2019/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for every g≥ 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.

Citations

• Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle
• Train tracks and the Gromov boundary of the complex of curves
• Small eigenvalues and thick-thin decomposition in negative curvature

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