Inspired by a recent work of Grove-Petersen in [GP18], where the authors studied Alexandrov spaces with largest possible boundary. We study Alexandrov spaces with lower curvature bound 1 and with small boundary. When the radius of X is \pi/2, and the boundary has diameter \pi/2, we classify the total space X.

中文翻译：

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带边界的正弯曲 Alexandrov 空间的刚性

受 Grove-Petersen 最近在 [GP18] 中的工作启发，作者研究了具有最大可能边界的 Alexandrov 空间。我们研究曲率下界为 1 且边界较小的 Alexandrov 空间。当X的半径为\pi/2，边界的直径为\pi/2时，我们对整个空间X进行分类。