Brunn-Minkowski and Reverse Isoperimetric Inequalities for Dual Quermassintegrals
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915312721461248 |
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| author | Sadovsky, Shay Zhang, Gaoyong |
| author_facet | Sadovsky, Shay Zhang, Gaoyong |
| contents | This paper establishes two new geometric inequalities in the dual Brunn-Minkowski theory. The first, originally conjectured by Lutwak, is the Brunn-Minkowski inequality for dual quermassintegrals of origin-symmetric convex bodies. The second, generalizing Ball's volume ratio inequality, is a reverse isoperimetric inequality: among all origin-symmetric convex bodies in John's position, the cube maximizes the dual quermassintegrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23748 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Brunn-Minkowski and Reverse Isoperimetric Inequalities for Dual Quermassintegrals Sadovsky, Shay Zhang, Gaoyong Metric Geometry Functional Analysis 52A40 This paper establishes two new geometric inequalities in the dual Brunn-Minkowski theory. The first, originally conjectured by Lutwak, is the Brunn-Minkowski inequality for dual quermassintegrals of origin-symmetric convex bodies. The second, generalizing Ball's volume ratio inequality, is a reverse isoperimetric inequality: among all origin-symmetric convex bodies in John's position, the cube maximizes the dual quermassintegrals. |
| title | Brunn-Minkowski and Reverse Isoperimetric Inequalities for Dual Quermassintegrals |
| topic | Metric Geometry Functional Analysis 52A40 |
| url | https://arxiv.org/abs/2505.23748 |