标题： 雷斯赫特尼亚克主要化与洛伦兹长度空间的离散上曲率界 显示英文标题

标题： Reshetnyak Majorisation and discrete upper curvature bounds for Lorentzian length spaces

摘要： 我们提出一个类似于Reshetnyak的Majorisation定理在具有上曲率限制的洛伦兹长度空间中的类似情况：给定两个未来指向的类时可求长曲线$\alpha$和$\beta$，在洛伦兹长度空间$X$中具有相同的端点，存在一个凸区域在$\mathbb{L}^2(K)$中，由两条未来指向的因果曲线$\bar \alpha$和$\bar \beta$围成，具有相同的端点，并且从该区域到$X$有一个1-反利普希茨映射，使得$\bar \alpha$和$\bar \beta$分别被$\tau$长度保持地映射到$\alpha$和$\beta$。 这个定理的一个特殊情况导致了通过四点配置对上曲率界限的有趣特征描述，这在离散设置中是真正适用的。 显示英文摘要

摘要： We present an analogue to the Majorisation Theorem of Reshetnyak in the setting of Lorentzian length spaces with upper curvature bounds: given two future-directed timelike rectifiable curves $\alpha$ and $\beta$ with the same endpoints in a Lorentzian length space $X$, there exists a convex region in $\mathbb{L}^2(K)$ bounded by two future-directed causal curves $\bar \alpha$ and $\bar \beta$ with the same endpoints and a 1-anti-Lipschitz map from that region into $X$ such that $\bar \alpha$ and $\bar \beta$ are respectively mapped $\tau$-length-preservingly onto $\alpha$ and $\beta$. A special case of this theorem leads to an interesting characterisation of upper curvature bounds via four-point configurations which is truly suitable for a discrete setting.