The Gauss Image Problem with Weak Aleksandrov Condition
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913521376165888 |
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| author | Semenov, Vadim |
| author_facet | Semenov, Vadim |
| contents | We introduce a relaxation of the Aleksandrov condition for the Gauss Image Problem. This weaker condition turns out to be a necessary condition for two measures to be related by a convex body. We provide several properties of the new condition. A solution to the Gauss Image Problem is obtained for the case when one of the measures is assumed to be discrete and the another measure is assumed to be absolutely continuous, under the new relaxed assumption. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_16778 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Gauss Image Problem with Weak Aleksandrov Condition Semenov, Vadim Metric Geometry 52A40, 35J96 (Primary) 52A20, 52A38, 52B11, 35J20 (Secondary) We introduce a relaxation of the Aleksandrov condition for the Gauss Image Problem. This weaker condition turns out to be a necessary condition for two measures to be related by a convex body. We provide several properties of the new condition. A solution to the Gauss Image Problem is obtained for the case when one of the measures is assumed to be discrete and the another measure is assumed to be absolutely continuous, under the new relaxed assumption. |
| title | The Gauss Image Problem with Weak Aleksandrov Condition |
| topic | Metric Geometry 52A40, 35J96 (Primary) 52A20, 52A38, 52B11, 35J20 (Secondary) |
| url | https://arxiv.org/abs/2210.16778 |