Alexandrov spaces with maximal radius

K. Grove, P. Petersen
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引用次数: 4

Abstract

Abstract. In this paper we prove several rigidity theorems related to and including Lytchak's problem. The focus is on Alexandrov spaces with \curv\geq1, nonempty boundary, and maximal radius \frac{\pi}{2}. We exhibit many such spaces that indicate that this class is remarkably flexible. Nevertheless, we also show that when the boundary is either geometrically or topologically spherical, then it is possible to obtain strong rigidity results. In contrast to this one can show that with general lower curvature bounds and strictly convex boundary only cones can have maximal radius. We also mention some connections between our problems and the positive mass conjectures. This paper is an expanded version and replacement of the two previous versions
最大半径的亚历山德罗夫空间
摘要本文证明了与Lytchak问题有关的几个刚性定理。重点讨论了具有\curv\geq 1、非空边界和最大半径\frac{\pi}{2}的Alexandrov空间。我们展示了许多这样的空间,表明这个类非常灵活。然而,我们也表明,当边界在几何上或拓扑上是球形时,则有可能获得强刚性结果。与此相反,我们可以证明,在一般下曲率边界和严格凸边界下,只有锥可以有最大半径。我们还提到了我们的问题与正质量猜想之间的一些联系。本文是对前两个版本的扩充和替换
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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