完备非紧流形上的Laplacian本性谱

Laplacian Essential Spectrum of a Complete Noncompact Riemannian Manifold

对完备非紧而形上的Laplacian本性谱进行了讨论，即若M是一个完备非紧流形，假设M有一个中心S,使得exps：NS→M是一个微分同胚（如果dimS＝0，我们假定S是M的极）．如果M的径向截曲率在M－S上，其绝对值满足一定条件，那么σ（－△）＝σess（－△）＝［0，∞）.

This paper is about the Laplacian essential spectrum of a complete noncompact Riemannian manifold, i.e. Let M be a complete noncompact manifold with a soul S suth that exp S': NS→M is a diffeomorphism (if dim S' =0, we assume S' is a pole of M). If the absolute value of the radial sectional curvatures satisfies some conditions on M - S', σ（－△）＝σess（－△）＝［o，∞）.