Characterizing intrinsic Lorentzian length spaces via τ-midpoints

2023/09/22 by Beran, Tobias, Rott, Felix · 1 citation
#51K10 #53C23 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2309.12962

Abstract

In metric geometry, the question of whether a distance metric is given by the length of curves can be decided via the existence of midpoints with respect to the metric d. We adapt a similar characterization to the setting of Lorentzian pre-length spaces. In particular, we show that a given space is strictly intrinsic provided it has τ-midpoints and merely intrinsic provided it has approximate τ-midpoints. Our approach is based on the null distance of C. Sormani and C. Vega.

Cited by

• Reshetnyak Majorisation and discrete upper curvature bounds for Lorentzian length spaces

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