Resonances for manifolds hyperbolic at infinity: optimal lower bounds on order of growth

2010/05/28 by David Borthwick, T. J. Christiansen, Borthwick, D. +5
Computer Science · Mathematics · #58J50 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1005.5400

openalex publication_date 2010/05/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Suppose that (X, g) is a conformally compact (n+1)-dimensional manifold that is hyperbolic at infinity in the sense that outside of a compact set K ⊂ X the sectional curvatures of g are identically equal to minus one. We prove that the counting function for the resolvent resonances has maximal order of growth (n+1) generically for such manifolds.

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