2008/07/25 by Samuel Tapie, Tapie, Samuel · 1 citation
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #math.DG
paper · pdf · doi:10.48550/arxiv.0807.4068
arxiv created 2008/07/25 · openalex publication_date 2008/07/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article presents some methods to control the bottom of the spectrum of the Laplacian λ0 on hyperbolic surfaces with infinite volume. Our first result bounds the λ0 of a geometrically finite surface in terms of the geometry of its convex core. We then focus on infinite type periodic hyperbolic surfaces built by gluing copies of a geometrically finite surface with boundary according to the plan of an infinite graph. We control the λ0 of the so-obtained infinite surfaces by constants coming from spectral properties of the building brick and combinatorial datae of the graph. We then use these methods to control the λ0 of two other kind of infinite type hyperbolic surfaces : those admitting a splitting into bounded pieces, and some riemannian coverings.