Bounds on Accumulation Rates of Eigenvalues on Manifolds with Degenerating Metrics

2003/11/14 by Jeffrey McGowan, McGowan, Jeffrey
Mathematics · #58A14 #58G25 #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP) #math.DG #math.SP #msc:58A14 #msc:58G25

paper · pdf · doi:10.48550/arxiv.math/0311249

10 pages

arxiv created 2004/01/09 · arxiv updated 2009/12/01

Abstract

We consider a family of manifolds with a class of degenerating warped product metrics g_ε=ρ(ε,t)^2adt² +ρ(ε,t)^2bds_M², with M compact, ρ homogeneous degree one, a ≤ -1 and b > 0. We study the Laplace operator acting on L² differential p-forms and give sharp accumulation rates for eigenvalues near the bottom of the essential spectrum of the limit manifold with metric g₀.

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