Abstract:We construct short retractions of a CAT(1) space to its small convex subsets. This construction provides an alternative geometric description of an analytic tool introduced by Wilfrid Kendall. Our construction uses a tractrix flow which can be defined as a gradient flow for a family of functions of certain type. In an appendix we prove a general existence result for gradient flows of time-dependent locally Lipschitz semiconcave functions, which is of independent interest.

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中文翻译：

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短暂收回CAT（1）空间

摘要：我们构造了CAT（1）空间向其小的凸子集的短缩回。这种构造提供了Wilfrid Kendall引入的分析工具的替代几何描述。我们的构造使用了tractrix流，可以将其定义为某些类型的函数族的梯度流。在附录中，我们证明了与时间有关的局部Lipschitz半凹函数的梯度流的一般存在性结果，该结果具有独立的意义。

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