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A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds

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arxiv 2401.03949 v2 pith:5WZ2HHEO submitted 2024-01-08 math.MG math-phmath.DGmath.MP

Fabio Cavalletti , Andrea Mondino This is my paper · ORCID
classification math.MGmath-phmath.DGmath.MP
keywords lorentzianinequalityriccispacestimelikeachronalalreadyarea
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abstract

The paper establishes a sharp and rigid isoperimetric-type inequality in Lorentzian signature under the assumption of Ricci curvature bounded below in the timelike directions. The inequality is proved in the high generality of Lorentzian pre-length spaces satisfying timelike Ricci lower bounds in a synthetic sense via optimal transport, the so-called $\mathsf{TCD}^e_p(K,N)$ spaces. The results are new already for smooth Lorentzian manifolds. Applications include an upper bound on the area of achronal hypersurfaces inside the interior of a black hole (original already in Schwarzschild) and an upper bound on the area of achronal hypersurfaces in cosmological spacetimes.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantitative Lorentzian isoperimetric inequalities in conical Minkowski spacetimes

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    Optimal stability estimates are established for Lorentzian isoperimetric inequalities of Bahn-Ehrlich and Cavalletti-Mondino using Fraenkel asymmetry, with quadratic or linear dependence and an upgrade to Hausdorff st...

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    gr-qc 2025-12 conditional novelty 6.0 of 10

    The cosmological volume function τ_V(p)=vol(I^-(p)) is C^1 temporal on future Cauchy developments and on finite-volume no-past-observer-horizon spacetimes, and it induces a canonical Wick-rotated Riemannian metric.

  3. New perspectives on the d'Alembertian from general relativity. An invitation

    math.DG 2025-01 conditional novelty 2.0 of 10

    A review of the p-d'Alembertian framework for Lorentzian distance functions, giving distributional comparison theorems across the timelike cut locus.

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