论文标题
在曲率上方有界限的地质完整空间中的极端子集
Extremal subsets in geodesically complete spaces with curvature bounded above
论文作者
论文摘要
我们介绍了一个极端子集中的概念，其曲率上面的曲率（即GCBA空间）。这是Alexandrov空间中极端子集的一个类似物，其曲率下面由Perelman和Petrunin引入。我们证明，在额外的假设下，GCBA空间中的拓扑奇异性构成了极端子集。我们还表现出GCBA空间中极端亚集的一些结构特性。
We introduce the notion of an extremal subset in a geodesically complete space with curvature bounded above, i.e., a GCBA space. This is an analogue of an extremal subset in an Alexandrov space with curvature bounded below introduced by Perelman and Petrunin. We prove that under an additional assumption the set of topological singularities in a GCBA space forms an extremal subset. We also exhibit some structural properties of extremal subsets in GCBA spaces.
