Small eigenvalues of hyperbolic surfaces with many cusps

2024/10/08 by Will Hide, Joe Thomas, Hide, Will +1
Mathematics · #58J50 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications #Spectral Theory (math.SP) #math.AP #math.SP #msc:58J50

paper · pdf · doi:10.48550/arxiv.2410.06093

openalex publication_date 2024/10/08 · openalex created_date 2025/10/10 · arxiv created 2026/07/30 · arxiv updated 2026/07/31 · openalex updated_date 2026/08/02

Abstract

We study topological lower bounds on the number of small Laplacian eigenvalues on hyperbolic surfaces. We show that for any a>0, there exists b>0 such that if g

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