Minkowski's successive minima in convex and discrete geometry
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913232298442752 |
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| author | Aliev, Iskander Henk, Martin |
| author_facet | Aliev, Iskander Henk, Martin |
| contents | In this short survey we want to present some of the impact of Minkowski's successive minima within Convex and Discrete Geometry. Originally related to the volume of an $o$-symmetric convex body, we point out relations of the successive minima to other functionals, as e.g., the lattice point enumerator or the intrinsic volumes and we present some old and new conjectures about them. Additionally, we discuss an application of successive minima to a version of Siegel's lemma. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00120 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Minkowski's successive minima in convex and discrete geometry Aliev, Iskander Henk, Martin Metric Geometry 52-02 In this short survey we want to present some of the impact of Minkowski's successive minima within Convex and Discrete Geometry. Originally related to the volume of an $o$-symmetric convex body, we point out relations of the successive minima to other functionals, as e.g., the lattice point enumerator or the intrinsic volumes and we present some old and new conjectures about them. Additionally, we discuss an application of successive minima to a version of Siegel's lemma. |
| title | Minkowski's successive minima in convex and discrete geometry |
| topic | Metric Geometry 52-02 |
| url | https://arxiv.org/abs/2304.00120 |