Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915143109050368 |
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| author | Huang, Yong Lutwak, Erwin Yang, Deane Zhang, Gaoyong |
| author_facet | Huang, Yong Lutwak, Erwin Yang, Deane Zhang, Gaoyong |
| contents | A longstanding question in the dual Brunn-Minkowski theory is what are the dual analogues of Federer's curvature measures for convex bodies. The answer to this is provided. This leads naturally to dual versions of Minkowski-type problems, which answer the question of what are necessary and sufficient conditions for a Borel measure to be a dual curvature measure of a convex body. Sufficient conditions, involving measure concentration, are established for the existence of solutions to these problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05436 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems Huang, Yong Lutwak, Erwin Yang, Deane Zhang, Gaoyong Metric Geometry 52A38 A longstanding question in the dual Brunn-Minkowski theory is what are the dual analogues of Federer's curvature measures for convex bodies. The answer to this is provided. This leads naturally to dual versions of Minkowski-type problems, which answer the question of what are necessary and sufficient conditions for a Borel measure to be a dual curvature measure of a convex body. Sufficient conditions, involving measure concentration, are established for the existence of solutions to these problems. |
| title | Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems |
| topic | Metric Geometry 52A38 |
| url | https://arxiv.org/abs/2502.05436 |