The growth rate of surface area measure for noncompact convex sets with prescribed asymptotic cone
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910922118791168 |
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| author | Semenov, Vadim Zhao, Yiming |
| author_facet | Semenov, Vadim Zhao, Yiming |
| contents | The Minkowski problem for a class of unbounded closed convex sets is considered. This is equivalent to a Monge-Ampère equation on a bounded convex open domain with possibly non-integrable given data. A complete solution (necessary and sufficient condition for existence and uniqueness) in dimension 2 is presented. In higher dimensions, partial results are demonstrated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18699 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The growth rate of surface area measure for noncompact convex sets with prescribed asymptotic cone Semenov, Vadim Zhao, Yiming Metric Geometry The Minkowski problem for a class of unbounded closed convex sets is considered. This is equivalent to a Monge-Ampère equation on a bounded convex open domain with possibly non-integrable given data. A complete solution (necessary and sufficient condition for existence and uniqueness) in dimension 2 is presented. In higher dimensions, partial results are demonstrated. |
| title | The growth rate of surface area measure for noncompact convex sets with prescribed asymptotic cone |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2409.18699 |