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arXiv · 2605.09101

Lorentzian coarea inequality

Hikaru Kubota
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Abstract

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 S\"{a}mann. 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.

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Hikaru Kubota. 2026-05-09. Lorentzian coarea inequality. https://arxiv.org/abs/2605.09101

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