On the spectral geometry of spaces with cone-like singularities.
On the spectral geometry of spaces with cone-like singularities.
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DOI：
10.1073/pnas.76.5.2103
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发表时间：
1979-05
影响因子：
11.1
通讯作者：
J. Cheeger
中科院分区：
文献类型：
--
作者：
J. Cheeger
本文将紧黎曼流形上拉普拉斯算子理论的一部分推广到具有奇异点的空间。虽然这种方法可以扩展到相当一般的空间，但本文将局限于具有锥状奇点的流形的情况。这些奇点在几何上可能是最简单的，但它们已经用来说明更一般情况下的典型新现象。此外，通过归纳论证，对于具有常曲率和完全测地线面的简单复形（如p.l.流形）的研究在很大程度上可以归结为对锥状奇异点的研究。
I describe an extension of a portion of the theory of the Laplace operator on compact riemannian manifolds to certain spaces with singularities. Although this approach can be extended to include quite general spaces, this paper will confine itself to the case of manifolds with cone-like singularities. These singularities are geometrically the simplest possible, but they already serve to illustrate new phenomena that are typical of the more general situation. Moreover, by inductive arguments, the study of simplicial complexes whose simplices have constant curvature and totally geodesic faces (e.g., p.l. manifolds) can in large measure be reduced to the study of cone-like singularities.