Strengthened volume inequalities for L_p zonoids of even isotropic measures
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arXiv
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| Format: | Preprint |
| Published: |
2016
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| _version_ | 1866910154834837504 |
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| author | Boroczky, Karoly J. Fodor, Ferenc Hug, Daniel |
| author_facet | Boroczky, Karoly J. Fodor, Ferenc Hug, Daniel |
| contents | We strengthen the volume inequalities for L_p zonoids of even isotropic measures and for their duals, which are due to Ball, Barthe and Lutwak, Yang, Zhang. Along the way, we prove a stronger version of the Brascamp-Lieb inequality for a family of functions that can approximate arbitrary well some Gaussians when equality holds. The special case p=\infty yields a stability version of the reverse isoperimetric inequality for centrally symmetric bodies. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1608_07084 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Strengthened volume inequalities for L_p zonoids of even isotropic measures Boroczky, Karoly J. Fodor, Ferenc Hug, Daniel Probability Metric Geometry We strengthen the volume inequalities for L_p zonoids of even isotropic measures and for their duals, which are due to Ball, Barthe and Lutwak, Yang, Zhang. Along the way, we prove a stronger version of the Brascamp-Lieb inequality for a family of functions that can approximate arbitrary well some Gaussians when equality holds. The special case p=\infty yields a stability version of the reverse isoperimetric inequality for centrally symmetric bodies. |
| title | Strengthened volume inequalities for L_p zonoids of even isotropic measures |
| topic | Probability Metric Geometry |
| url | https://arxiv.org/abs/1608.07084 |