On the monotonicity of weighted perimeters of convex bodies
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913303269212160 |
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| author | Saracco, Giorgio Stefani, Giorgio |
| author_facet | Saracco, Giorgio Stefani, Giorgio |
| contents | We prove that, among weighted isotropic perimeters, only constant multiples of the Euclidean perimeter satisfy the monotonicity property on nested convex bodies. Although the analogous result fails for general weighted anisotropic perimeters, a similar characterization holds for radially-weighted anisotropic densities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07770 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the monotonicity of weighted perimeters of convex bodies Saracco, Giorgio Stefani, Giorgio Metric Geometry 52A20, 52A38, 52A40 We prove that, among weighted isotropic perimeters, only constant multiples of the Euclidean perimeter satisfy the monotonicity property on nested convex bodies. Although the analogous result fails for general weighted anisotropic perimeters, a similar characterization holds for radially-weighted anisotropic densities. |
| title | On the monotonicity of weighted perimeters of convex bodies |
| topic | Metric Geometry 52A20, 52A38, 52A40 |
| url | https://arxiv.org/abs/2306.07770 |