Boundary restricted Brunn-Minkowski inequalities
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911969852784640 |
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| author | Artstein-Avidan, Shiri Falah, Tomer Slomka, Boaz A. |
| author_facet | Artstein-Avidan, Shiri Falah, Tomer Slomka, Boaz A. |
| contents | In this paper we explore questions regarding the Minkowski sum of the boundaries of convex sets. Motivated by a question suggested to us by V.~Milman regarding the volume of $\partial K+ \partial T$ where $K$ and $T$ are convex bodies, we prove sharp volumetric lower bounds for the Minkowski average of the boundaries of sets with connected boundary, as well as some related results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15293 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Boundary restricted Brunn-Minkowski inequalities Artstein-Avidan, Shiri Falah, Tomer Slomka, Boaz A. Metric Geometry 52A20, 52A38, 52A40 In this paper we explore questions regarding the Minkowski sum of the boundaries of convex sets. Motivated by a question suggested to us by V.~Milman regarding the volume of $\partial K+ \partial T$ where $K$ and $T$ are convex bodies, we prove sharp volumetric lower bounds for the Minkowski average of the boundaries of sets with connected boundary, as well as some related results. |
| title | Boundary restricted Brunn-Minkowski inequalities |
| topic | Metric Geometry 52A20, 52A38, 52A40 |
| url | https://arxiv.org/abs/2306.15293 |