Compactness of Relatively Isospectral Sets of Surfaces Via Conformal Surgeries

2012/06/26 by Pierre Albin, Albin, Pierre, Clara L. Aldana +3
Mathematics · #58J35 #58J50 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1206.6077

openalex publication_date 2012/06/26 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We introduce a notion of relative isospectrality for surfaces with boundary\nhaving possibly non-compact ends either conformally compact or asymptotic to\ncusps. We obtain a compactness result for such families via a conformal surgery\nthat allows us to reduce to the case of surfaces hyperbolic near infinity\nrecently studied by Borthwick and Perry, or to the closed case by Osgood,\nPhillips and Sarnak if there are only cusps.\n

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