The limit spaces of two-dimensional manifolds with uniformly bounded integral curvature
The limit spaces of two-dimensional manifolds with uniformly bounded integral curvature
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一致有界积分曲率二维流形的极限空间
DOI：
10.1090/s0002-9947-99-02103-0
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
T. Shioya
中科院分区：
文献类型：
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作者：
T. Shioya
研究了一类具有一致有界直径和全绝对曲率的闭2维黎曼流形。我们的第一个定理指出，这类流形是关于Gromov-Hausdorff距离的预紧。本文的目的是完全刻画流形类的所有极限空间的拓扑结构，这些流形一般不是拓扑流形，甚至可能不是局部2-连通的。我们还研究了当p ≥ 1时具有Lp-曲率界的2-流形的极限。
We study the class of closed 2-dimensional Riemannian manifolds with uniformly bounded diameter and total absolute curvature. Our first theorem states that this class of manifolds is precompact with respect to the Gromov-Hausdorff distance. Our goal in this paper is to completely characterize the topological structure of all the limit spaces of the class of manifolds, which are, in general, not topological manifolds and even may not be locally 2-connected. We also study the limit of 2-manifolds with Lp-curvature bound for p ≥ 1.