arXiv subjects

Hikaru Kubota

Publications and source records attributed to Hikaru Kubota.

2 recordsLinked to original sources

arXiv2026

Lorentzian coarea inequality

In this article, we introduce the notion of locally uniformly d-controlling map between Lorentzian pre-length spaces which is preserving the diameters of causal diamonds, and through that we establish the coarea inequality for Lorentzian Hausdorff measure which is introduced by McCann and Sämann. Besides that we get a covering lemma for subsets in a Lorentzian pre-length space with a new local assumption named the local causal enlargement property, which enables us to enlarge causal diamonds.

math.MG↗

arXiv2025

Volume comparison by timelike Lipschitz maps

In this article, we introduce a modification of the timelike Hausdorff measure VN defined by McCann and Samann on Lorentzian pre-length spaces. We write the modification of VN as WN. We establish volume comparison inequalities by causality preserving and timelike Lipschitz maps for VN and WN, and discuss basic properties of both VN and WN. Moreover, we show the coincidence of WN and VN on smooth spacetimes and some Lorentzian pre-length spaces, and construct some examples of timelike Lipschitz maps and causality preserving maps.

math.DG↗