Espectro de variedades completas e não-compactas

Abstract

On this work we study the espectrum of Laplace-Beltrami operator on the warped Riemannian manifold Mⁿ = R Xᵣ Sⁿ⁻¹, whose warping function is smooth, positive, periodic, with period a and satisfies r₀ = min r(t) < √n - 1a/π. We show that spectrum there no eingevalue, is formed by a union of closed intervals, and, from the peridicity of r, using the classical Hill's Equations Theory, we conclude the existence of gaps.