On Geometry of Flat Complete Strictly Causal Lorentzian Manifolds

洛伦兹长度空间的粘合与因果阶梯

Gluing of Lorentzian length spaces and the causal ladder

本文研究洛伦兹长度空间在粘合操作下保持结构性质的条件，并给出保留因果阶梯多个层级的判据，同时讨论难以传递的因果性质。

洛伦兹共面积不等式

Lorentzian coarea inequality

本文引入了在洛伦兹预长度空间之间保持因果钻石直径的局部均匀d-控制映射的概念，并通过该概念建立了由McCann和Sämann引入的洛伦兹霍尔德测度的共面积不等式，同时得到了一个覆盖引理，该引理通过新的局部假设——局部因果扩展性质，使因果钻石得以扩展。

On flat complete causal Lorentzian manifolds

We describe up to finite coverings causal flat affine complete Lorentzian manifolds such that the past and the future of any point are closed near this point. We say that these manifolds are strictly causal. In particular, we prove that their fundamental groups are virtually abelian. In dimension 4, there is only one, up to a scaling factor, strictly causal manifold which is not globally hyperbolic. For a generic point of this manifold, either the past or the future is not closed and contains a lightlike straight line.

On the space of compact diamonds of Lorentzian length spaces

In this work we introduce the taxicab and uniform products for Lorentzian pre-length spaces. We further use these concepts to endow the space $D(R\times_T X)$ of causal diamonds with a Lorentzian length space structure, closely relating its causal properties with its geometry as a metric space furnished with its associated Hausdorff distance. Among the general results, we show that this space is geodesic and globally hyperbolic for complete $X$.

微分闵可夫斯基性对于具有连续洛伦兹度量的流形

Infinitesimal Minkowskianity for manifolds with continuous Lorentzian metrics

本文证明在因果简单条件下，由光滑流形M和连续洛伦兹度量g产生的度量测时空是微分闵可夫斯基的。

零距离与洛伦兹长度空间的收敛性

Null distance and convergence of Lorentzian length spaces

本文将零距离概念从光滑时空推广到洛伦兹长度空间，并基于该距离研究扭曲积洛伦兹长度空间的Gromov-Hausdorff收敛，首次证明了其与合成曲率界的相容性。