We show that bounded self-contracted curves are rectifiable in metric spaces with weak lower curvature bound in a sense we introduce in this article. This class of spaces is wide and includes, for example, finite-dimensional Alexandrov spaces of curvature bounded below and Berwald spaces of nonnegative flag curvature. (To be more precise, our condition is regarded as a strengthened doubling condition and holds also for a certain class of metric spaces with upper curvature bound.) We also provide the non-embeddability of large snowflakes into (balls in) metric spaces in the same class. We follow the strategy of the last author's previous paper based on the small rough angle condition, where spaces with upper curvature bound are considered. The results in this article show that such a strategy applies to spaces with lower curvature bound as well.

中文翻译：

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弱曲率下界空间中的自收缩曲线

我们证明了有界自收缩曲线在具有弱下曲率界的度量空间中是可矫正的，在我们在本文中介绍的某种意义上。这类空间范围很广，例如包括下界曲率的有限维 Alexandrov 空间和非负旗曲率的 Berwald 空间。（更准确地说，我们的条件被认为是一个加强的加倍条件，并且对于某一类具有上曲率界的度量空间也成立。）我们还提供了大雪花到（球在）度量空间中的不可嵌入性。同班。我们遵循上一作者之前论文的基于小粗糙角条件的策略，其中考虑了具有上曲率边界的空间。本文中的结果表明，这种策略也适用于曲率边界较低的空间。