标题： 一个合成洛伦兹卡当-哈达玛定理 显示英文标题

标题： A synthetic Lorentzian Cartan-Hadamard theorem

摘要： 我们提出了并证明了一个合成的洛伦兹型Cartan-Hadamard定理。 该结果既将S. Alexander和R. Bishop在局部凸度量空间中建立的相应陈述转移到了洛伦兹型设置，又同时将J. Beem和P. Ehrlich讨论的光滑洛伦兹型定理推广到了最近建立的合成洛伦兹几何框架。 我们的方法基于洛伦兹（预-长度）空间的一个适当局部凹性的概念，这使我们在全局双曲性和未来单连通性的额外假设下，能够建立任何一对类时相关点之间的类时测地线的存在性和唯一性。 我们还提供了在洛伦兹长度空间设定下我们凹性概念的全局化结果，并应用我们的结果来获得非负上类时曲率界限的全局化陈述。 显示英文摘要

摘要： We formulate and prove a synthetic Lorentzian Cartan-Hadamard theorem. This result both transfers the corresponding statement for locally convex metric spaces established by S. Alexander and R. Bishop to the Lorentzian setting, and simultaneously generalizes the smooth Lorentzian theorem discussed by J. Beem and P. Ehrlich to the recently established framework of synthetic Lorentzian geometry. Our approach is based on an appropriate notion of local concavity for Lorentzian (pre-)length spaces, which allows us to establish existence and uniqueness of timelike geodesics between any pair of timelike related points under the additional assumptions of global hyperbolicity and future one-connectedness. We also provide a globalization result for our notion of concavity in the setting of Lorentzian length spaces, and apply our results to obtain a globalization statement for nonnegative upper timelike curvature bounds.