The strong Brunn--Minkowski inequality and its equivalence with the CD condition
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917687035166720 |
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| author | Magnabosco, Mattia Portinale, Lorenzo Rossi, Tommaso |
| author_facet | Magnabosco, Mattia Portinale, Lorenzo Rossi, Tommaso |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_01494 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The strong Brunn--Minkowski inequality and its equivalence with the CD condition Magnabosco, Mattia Portinale, Lorenzo Rossi, Tommaso Metric Geometry 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. |
| title | The strong Brunn--Minkowski inequality and its equivalence with the CD condition |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2210.01494 |