On Topological Upper-Bounds on the Number of Small Cuspidal Eigenvalues of Hyperbolic Surfaces of Finite Area
نویسندگان
چکیده
ior of small cuspidal eigenpairs of ΔS. In Theorem 1.7, we describe limiting behavior of these eigenpairs on surfaces Sm ∈Mg,n when (Sm) converges to a point in M̄g,n. Then, we consider the ith cuspidal eigenvalue, λc i (S), of S∈Mg,n. Since noncuspidal eigenfunctions (residual eigenfunctions or generalized eigenfunctions) may converge to cuspidal eigenfunctions, it is not known if λc i (S) is a continuous function. However, applying Theorem 1.7 we prove that, for all k≥ 2g− 2, the sets
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