A new infinitesimal form of the Prékopa-Leindler inequality with multiplicative structure and applications
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915819721588736 |
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| author | Armeniakos, Sotiris Ulivelli, Jacopo |
| author_facet | Armeniakos, Sotiris Ulivelli, Jacopo |
| contents | By differentiating a concavity principle arising from the Prékopa-Leindler inequality, we obtain a statement simultaneously strengthening the weighted boundary Poincaré inequality and the Brascamp-Lieb variance inequality. The resulting inequality possesses a multiplicative structure, which we exploit to develop an alternative to the (by now classical) $L_2$ method in the study of geometric and analytic inequalities. We apply this approach to derive a stability estimate for the weighted Poincaré inequality and to investigate the dimensional Brunn-Minkowski conjecture. In particular, in the latter setting, we obtain new reformulations together with several partial results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10812 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A new infinitesimal form of the Prékopa-Leindler inequality with multiplicative structure and applications Armeniakos, Sotiris Ulivelli, Jacopo Functional Analysis Metric Geometry 52A40, 52A20, 28C20, 46N20, 47F10 By differentiating a concavity principle arising from the Prékopa-Leindler inequality, we obtain a statement simultaneously strengthening the weighted boundary Poincaré inequality and the Brascamp-Lieb variance inequality. The resulting inequality possesses a multiplicative structure, which we exploit to develop an alternative to the (by now classical) $L_2$ method in the study of geometric and analytic inequalities. We apply this approach to derive a stability estimate for the weighted Poincaré inequality and to investigate the dimensional Brunn-Minkowski conjecture. In particular, in the latter setting, we obtain new reformulations together with several partial results. |
| title | A new infinitesimal form of the Prékopa-Leindler inequality with multiplicative structure and applications |
| topic | Functional Analysis Metric Geometry 52A40, 52A20, 28C20, 46N20, 47F10 |
| url | https://arxiv.org/abs/2602.10812 |