Functional Liftings of Restricted Geometric Inequalities
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| author | Malliaris, Andreas Melbourne, James Roberto, Cyril Roysdon, Michael |
| author_facet | Malliaris, Andreas Melbourne, James Roberto, Cyril Roysdon, Michael |
| contents | We investigate what we term "generalized sup-convolutions". We show that functional inequalities that enjoy an interpretation as sup-convolution inequalities can be deduced from the special case of indicator functions corresponding to a geometric inequality. As consequences we derive a Borell-Brascamp Lieb inequality for the Gaussian Brunn-Minkowski inequality and give a functional analog of the log-Brunn Minkowski conjecture. Though we focus on Euclidean applications, our results are general and can be directly applied in more abstract settings, like groups or even topological measure spaces without algebraic structure, we instantiate this claim with a Borell-Brascamp-Lieb type inequality for nilpotent Lie groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functional Liftings of Restricted Geometric Inequalities Malliaris, Andreas Melbourne, James Roberto, Cyril Roysdon, Michael Functional Analysis Metric Geometry Probability We investigate what we term "generalized sup-convolutions". We show that functional inequalities that enjoy an interpretation as sup-convolution inequalities can be deduced from the special case of indicator functions corresponding to a geometric inequality. As consequences we derive a Borell-Brascamp Lieb inequality for the Gaussian Brunn-Minkowski inequality and give a functional analog of the log-Brunn Minkowski conjecture. Though we focus on Euclidean applications, our results are general and can be directly applied in more abstract settings, like groups or even topological measure spaces without algebraic structure, we instantiate this claim with a Borell-Brascamp-Lieb type inequality for nilpotent Lie groups. |
| title | Functional Liftings of Restricted Geometric Inequalities |
| topic | Functional Analysis Metric Geometry Probability |
| url | https://arxiv.org/abs/2508.15247 |