中轴与冲突集的Kuratowski收敛性
The Kuratowski convergence of medial axes and conflict sets
摘要：
本文分下列两部分:1.在第一部分中，我们研究了变形下连通完备黎曼流形$\mathcal{M}$中闭集的中轴（骨架）的行为。第二篇是关于冲突集的类似研究。我们对变形过程应用了一种新的方法。我们不把它看作是从初始状态到最终状态的“跳跃”，而是把它看作是一个连续的过程，用集合的库拉托夫斯基收敛来表示（因此，与其他作者不同，我们不需要变形的任何规则性）。我们的主要“中轴内半连续性”结果已经证明是有用的，因为它被用来计算中轴的切锥，并在奇异性理论中得到应用。
英文摘要：
This paper consists of two parts. In the first one we study the behaviour of medial axes (skeletons) of closed sets in a connected complete Riemannian manifold $\mathcal{M}$ under deformations. The second one is devoted to a similar study of conflict sets. We apply a new approach to the deformation process. Instead of seeing it as a `jump' from the initial to the final state, we perceive it as a continuous process, expressed using the Kuratowski convergence of sets (hence, unlike other authors, we do not require any regularity of the deformation). Our main `medial axis inner semi-continuity' result has already proved useful, as it was used to compute the tangent cone of the medial axis with application in singularity theory.
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