Bounds on Accumulation Rates of Eigenvalues on Manifolds with Degenerating Metrics

Details Bounds on Accumulation Rates of Eigenvalues on Manifolds with Degenerating Metrics Bounds on Accumulation Rates of Eigenvalues on Manifolds with Degenerating Metrics

2003-11-14

arxiv.org/abs/math/0311249v3

Mathematics

Differential Geometry

10 pages

Scientific paper

We consider a family of manifolds with a class of degenerating warped product metrics $g_\epsilon=\rho(\epsilon,t)^{2a}dt^2 +\rho(\epsilon,t)^{2b}ds_M^2$, with $M$ compact, $\rho$ 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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