Abstract:We construct complete finite-area noncompact hyperbolic surfaces with linearly many cusps and a uniform spectral gap. More precisely, for every \(\theta>0\), we construct a sequence \(S_{g,n(g)}\in\mathcal{M}_{g,n(g)}\) such that \(\lim\limits_{g\to\infty}\frac{n(g)}{g}=\theta\) and the spectrum of the Laplacian has a uniform gap above zero. The construction is based on explicit expanding \((1,3)\)-graphs, viewed as combinatorial skeletons for pants decompositions. We also establish a Steklov-type upper bound showing that expansion cannot persist when the number of boundary vertices is much larger than the genus.
From: Qi Guo [view email]
[v1]
Tue, 22 Jul 2025 17:44:22 UTC (383 KB)
[v2]
Mon, 28 Jul 2025 11:56:45 UTC (383 KB)
[v3]
Thu, 6 Aug 2026 20:30:11 UTC (366 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。