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Mathematics > Metric Geometry

arXiv:2210.01494 (math)
[Submitted on 4 Oct 2022]

Title:The strong Brunn--Minkowski inequality and its equivalence with the CD condition

Authors:Mattia Magnabosco, Lorenzo Portinale, Tommaso Rossi
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Abstract:In the setting of essentially non-branching metric measure spaces, we prove the equivalence between the curvature dimension condition CD(K,N), in the sense of Lott--Sturm--Villani, and a newly introduced notion that we call strong Brunn--Minkowski inequality SBM(K,N). This condition is a reinforcement of the generalized Brunn--Minkowski inequality BM(K,N), which is known to hold in CD(K,N) spaces. Our result is a first step towards providing a full equivalence between the CD(K,N) condition and the validity of BM(K,N), which we have recently proved in the framework of weighted Riemannian manifolds.
Subjects: Metric Geometry (math.MG)
Cite as: arXiv:2210.01494 [math.MG]
  (or arXiv:2210.01494v1 [math.MG] for this version)
  https://doi.org/10.48550/arXiv.2210.01494
Related DOI: https://doi.org/10.1142/S0219199724500251

Submission history

From: Lorenzo Portinale [view email]
[v1] Tue, 4 Oct 2022 09:50:46 UTC (24 KB)
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