Empirical forms of the Petty projection inequality
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909445874778112 |
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| author | Paouris, Grigoris Pivovarov, Peter Tatarko, Kateryna |
| author_facet | Paouris, Grigoris Pivovarov, Peter Tatarko, Kateryna |
| contents | The Petty projection inequality is a fundamental affine isoperimetric principle for convex sets. It has shaped several directions of research in convex geometry which forged new connections between projection bodies, centroid bodies, and mixed volume inequalities. We establish several different empirical forms of the Petty projection inequality by re-examining these key relationships from a stochastic perspective. In particular, we derive sharp extremal inequalities for several multiple-entry functionals of random convex sets, including mixed projection bodies and mixed volumes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00253 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Empirical forms of the Petty projection inequality Paouris, Grigoris Pivovarov, Peter Tatarko, Kateryna Metric Geometry The Petty projection inequality is a fundamental affine isoperimetric principle for convex sets. It has shaped several directions of research in convex geometry which forged new connections between projection bodies, centroid bodies, and mixed volume inequalities. We establish several different empirical forms of the Petty projection inequality by re-examining these key relationships from a stochastic perspective. In particular, we derive sharp extremal inequalities for several multiple-entry functionals of random convex sets, including mixed projection bodies and mixed volumes. |
| title | Empirical forms of the Petty projection inequality |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2501.00253 |