Bounds on Accumulation Rates of Eigenvalues on Manifolds with Degenerating Metrics

الأصل · EN

We consider a family of manifolds with a class of degenerating warped product metrics gε=ρ(ε,t)²ᵃdt² +ρ(ε,t)²ᵇdsₘ², 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.