In synthetic Lorentzian spaces, the timelike curvature dimension condition TCD_q(K,N) is equivalent to the timelike Brunn-Minkowski inequality TBM_q(K,N) in the q-essentially non-branching case, with a similar equivalence for the entropic version.
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Rigidity theorem for the Borell-Brascamp-Lieb inequality is shown on weighted Riemannian manifolds, generalizing Balogh-Kristály to the weighted setting.
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The equivalence between timelike Ricci curvature and the timelike Brunn Minkowski inequality on synthetic Lorentzian spaces
In synthetic Lorentzian spaces, the timelike curvature dimension condition TCD_q(K,N) is equivalent to the timelike Brunn-Minkowski inequality TBM_q(K,N) in the q-essentially non-branching case, with a similar equivalence for the entropic version.
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Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds
Rigidity theorem for the Borell-Brascamp-Lieb inequality is shown on weighted Riemannian manifolds, generalizing Balogh-Kristály to the weighted setting.