A Second Eigenvalue Bound for the Dirichlet Laplacian in Hyperbolic Space
نویسنده
چکیده
Let Ω be some domain in the hyperbolic space Hn (with n ≥ 2) and S1 the geodesic ball that has the same first Dirichlet eigenvalue as Ω. We prove the Payne-Pólya-Weinberger conjecture for Hn, i.e., that the second Dirichlet eigenvalue on Ω is smaller or equal than the second Dirichlet eigenvalue on S1. We also prove that the ratio of the first two eigenvalues on geodesic balls is a decreasing function of the radius.
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تاریخ انتشار 2005