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We characterize the null energy condition for an $(n+1)$-dimensional Lorentzian manifold in terms of convexity of the relative $(n-1)$-Renyi entropy along displacement interpolations on null hypersurfaces.
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Robert J. McCann, Displacement convexity of Boltzmann’s entropy characterizes the strong energy condition from general relativity , Camb. J. Math. 8
2020
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2021
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Fabio Cavalletti and Andrea Mondino, A review of Lorentzian synthetic theory of timelike Ricci curvature bounds , Gen. Relativ. Gravitation 54
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Robert J. McCann and Clemens Sämann, A Lorentzian analog for Hausdorff dimension and measure , Pure Appl. Anal. 4
2022
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Andrea Mondino and Stefan Suhr, An optimal transport formulation of the einstein equations of general relativity , Journal of the European Mathematical Society (2022)
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2020
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Christian Ketterer, The Heintze-Karcher inequality for metric measure spaces , Proc. Am. Math. Soc. 148
2020
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Mathias Braun, Rényi’s entropy on lorentzian spaces. timelike curvature-dimension conditions
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2022
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