The Discrete Gauss Image Problem
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866913521381408768 |
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| author | Semenov, Vadim |
| author_facet | Semenov, Vadim |
| contents | We study the Discrete Gauss Image Problem, a generalization of Aleksandrov's classical question on the existence of convex bodies with prescribed integral curvature. We introduce a combinatorial problem called the Assignment Problem and show its equivalence to the Discrete Gauss Image Problem. We establish sufficient (and nearly necessary) geometric conditions on measures that solve both problems. Additionally, we provide new discrete interpretations of some classical concepts related to Aleksandrov's integral curtvature, such as, for example, connecting Aleksandrov relation to Hall's Marriage Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_16974 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Discrete Gauss Image Problem Semenov, Vadim Metric Geometry Combinatorics 52A40, 35J96 (Primary) 52A20, 52A38, 52B11, 35J20, 35J96 (Secondary) We study the Discrete Gauss Image Problem, a generalization of Aleksandrov's classical question on the existence of convex bodies with prescribed integral curvature. We introduce a combinatorial problem called the Assignment Problem and show its equivalence to the Discrete Gauss Image Problem. We establish sufficient (and nearly necessary) geometric conditions on measures that solve both problems. Additionally, we provide new discrete interpretations of some classical concepts related to Aleksandrov's integral curtvature, such as, for example, connecting Aleksandrov relation to Hall's Marriage Theorem. |
| title | The Discrete Gauss Image Problem |
| topic | Metric Geometry Combinatorics 52A40, 35J96 (Primary) 52A20, 52A38, 52B11, 35J20, 35J96 (Secondary) |
| url | https://arxiv.org/abs/2210.16974 |