叶空间的边界猜想
The Boundary Conjecture for Leaf Spaces
摘要：
我们证明了一个轨道空间的边界或更一般的叶空间的奇异黎曼叶状是一个亚历山德罗夫空间在其内在的度量，它的下曲率界是叶空间。建立了具有最大边界体积的正曲叶空间的刚性定理，该定理在边界问题的证明中起着关键作用。
英文摘要：
We prove that the boundary of an orbit space or more generally a leaf space of a singular Riemannian foliation is an Alexandrov space in its intrinsic metric, and that its lower curvature bound is that of the leaf space. A rigidity theorem for positively curved leaf spaces with maximal boundary volume is also established and plays a key role in the proof of the boundary problem.
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