Gromov's reconstruction theorem and measured Gromov-Hausdorff convergence in Lorentzian geometry

Mathias Braun; Clemens Sämann

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arXiv · 2506.10852

Gromov's reconstruction theorem and measured Gromov-Hausdorff convergence in Lorentzian geometry

Mathias Braun·Clemens Sämann

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Abstract

We establish Gromov's celebrated reconstruction theorem in Lorentzian geometry. Alongside this result, we introduce and study a natural concept of isomorphy of normalized bounded Lorentzian metric measure spaces. We outline applications to the spacetime reconstruction problem from causal set theory. Lastly, we propose three notions of convergence of (isomorphism classes of) normalized bounded Lorentzian metric measure spaces, for which we prove several fundamental properties.

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Mathias Braun, Clemens Sämann. 2025-06-12. Gromov's reconstruction theorem and measured Gromov-Hausdorff convergence in Lorentzian geometry. https://arxiv.org/abs/2506.10852

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