Abstract
AbstractWe introduce an analogue to the amalgamation of metric spaces into the setting of Lorentzian pre-length spaces. This provides a very general process of constructing new spaces out of old ones. The main application in this work is an analogue of the gluing theorem of Reshetnyak for CAT(k) spaces, which roughly states that gluing is compatible with upper curvature bounds. Due to the absence of a notion of spacelike distance in Lorentzian pre-length spaces we can only formulate the theorem in terms of (strongly causal) spacetimes viewed as Lorentzian length spaces.
Publisher
Springer Science and Business Media LLC
Reference20 articles.
1. Aké Hau, L., Cabrera Pacheco, A.J., Solis, D.A.: On the causal hierarchy of Lorentzian length spaces. Classical Quantum Gravity 37(21), 215013 (2020)
2. Alexander, S.B., Bishop, R.L.: Lorentz and semi-Riemannian spaces with Alexandrov curvature bounds. Commun. Anal. Geom. 16(2), 251–282 (2008)
3. Alexander, S. B., Graf, M., Kunzinger, M., Sämann, C.: Generalized cones as Lorentzian length spaces: causality, curvature, and singularity theorems. Commun. Anal. Geom. (2019). to appear, Preprint: arXiv:1909.09575
4. Alexander, S.B., Kapovitch, V., Petrunin, A.: An Invitation to Alexandrov Geometry: CAT(0) spaces. SpringerBriefs in Mathematics. Springer, Berlin (2019)
5. Beran, T.: Lorentzian length spaces. Master’s thesis, University of Vienna (2020). https://phaidra.univie.ac.at/open/o:1363059
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献