Cheeger constants of hyperbolic reflection groups and Maass cusp forms of small eigenvalues

Analytic torsion and R-torsion of Witt representations on manifolds with cusps

We establish a Cheeger-Muller theorem for unimodular representations satisfying a Witt condition on a noncompact manifold with cusps. This class of spaces includes all non-compact hyperbolic spaces of finite volume, but we do not assume that the metric has constant curvature nor that the link of the cusp is a torus. We use renormalized traces in the sense of Melrose to define the analytic torsion and we relate it to the intersection R-torsion of Dar of the natural compactification to a stratified space. Our proof relies on our recent work on the behavior of the Hodge Laplacian spectrum on a cl…

具有许多尖点的随机双曲面的任意小谱隙

Arbitrarily small spectral gaps for random hyperbolic surfaces with many cusps

本文研究了当亏格 $g$ 趋于无穷且穿孔数 $n(g)$ 增长慢于 $g$ 时，赋予 Weil-Petersson 度量的随机双曲面模空间中 Cheeger 常数与谱隙的渐近行为。