arXiv math/03112492003-11math.DGmath.SP

Bounds on Accumulation Rates of Eigenvalues on Manifolds with Degenerating Metrics

Jeffrey McGowan

备注：: 10 pages

英文摘要：

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

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