Monotonicity of the deficit in the local log-Brunn-Minkowski inequality
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911248525819904 |
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| author | Wang, Shouda |
| author_facet | Wang, Shouda |
| contents | We establish a monotonicity property of the deficit associated with the local log-Brunn-Minkowski inequality (LLBM) under addition of line segments. As a corollary, if the LLBM holds for a convex body K, then it also holds for K+Z for any zonoid Z, which in particular yields a new proof of the inequality for zonoids. Moreover, assuming the LLBM is valid, we prove that equality in the LLBM for smooth convex bodies with $C^2$ support functions occurs only for homothetic bodies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19061 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monotonicity of the deficit in the local log-Brunn-Minkowski inequality Wang, Shouda Metric Geometry Differential Geometry We establish a monotonicity property of the deficit associated with the local log-Brunn-Minkowski inequality (LLBM) under addition of line segments. As a corollary, if the LLBM holds for a convex body K, then it also holds for K+Z for any zonoid Z, which in particular yields a new proof of the inequality for zonoids. Moreover, assuming the LLBM is valid, we prove that equality in the LLBM for smooth convex bodies with $C^2$ support functions occurs only for homothetic bodies. |
| title | Monotonicity of the deficit in the local log-Brunn-Minkowski inequality |
| topic | Metric Geometry Differential Geometry |
| url | https://arxiv.org/abs/2510.19061 |