Kubota-type formulas and supports of mixed measures
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915721153347584 |
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| author | Hug, Daniel Mussnig, Fabian Ulivelli, Jacopo |
| author_facet | Hug, Daniel Mussnig, Fabian Ulivelli, Jacopo |
| contents | Kubota's integral formula expresses the intrinsic volumes of a convex body as averages over its projections onto linear subspaces. In this work, we introduce a new class of Kubota-type formulas for mixed area measures adapted to rotations around a fixed axis, which encode a crucial disintegration property. Our construction is motivated by applications to valuations on convex functions. In the latter framework, we obtain corresponding statements for (conjugate) mixed Monge-Ampère measures. As a by-product, we characterize supports of mixed area and mixed Monge-Ampère measures, thereby confirming a special case of a conjecture by Schneider. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16371 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kubota-type formulas and supports of mixed measures Hug, Daniel Mussnig, Fabian Ulivelli, Jacopo Metric Geometry Functional Analysis 52A39 (Primary) 52A41, 52A20, 52B45 (Secondary) Kubota's integral formula expresses the intrinsic volumes of a convex body as averages over its projections onto linear subspaces. In this work, we introduce a new class of Kubota-type formulas for mixed area measures adapted to rotations around a fixed axis, which encode a crucial disintegration property. Our construction is motivated by applications to valuations on convex functions. In the latter framework, we obtain corresponding statements for (conjugate) mixed Monge-Ampère measures. As a by-product, we characterize supports of mixed area and mixed Monge-Ampère measures, thereby confirming a special case of a conjecture by Schneider. |
| title | Kubota-type formulas and supports of mixed measures |
| topic | Metric Geometry Functional Analysis 52A39 (Primary) 52A41, 52A20, 52B45 (Secondary) |
| url | https://arxiv.org/abs/2401.16371 |