Tracking eigenvalues to the frontier of moduli space I: Convergence and spectral accumulation

2001/02/28 by Chris Judge, Judge, Chris
Mathematics · #35P20 #58G25 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.DG #math.SP #msc:35P20 #msc:58G25

paper · pdf · doi:10.48550/arxiv.math/0102219

openalex publication_date 2001/02/28 · arxiv created 2001/05/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the limiting behavior of eigenfunctions/eigenvalues of the Laplacian of a family of Riemannian metrics that degenerates on a hypersurface. Our results generalize earlier work concerning the degeneration of hyperbolic surfaces.

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