On area-minimizing subgraphs in integer lattices
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866913398090891264 |
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| author | He, Zunwu Hua, Bobo |
| author_facet | He, Zunwu Hua, Bobo |
| contents | We introduce area-minimizing subgraphs in an infinite graph via the formulation of functions of bounded variations initiated by De Giorgi. We classify area-minimizing subgraphs in the two-dimensional integer lattice up to isomorphisms, and prove general geometric properties for those in high-dimensional cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13277 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On area-minimizing subgraphs in integer lattices He, Zunwu Hua, Bobo Combinatorics Differential Geometry We introduce area-minimizing subgraphs in an infinite graph via the formulation of functions of bounded variations initiated by De Giorgi. We classify area-minimizing subgraphs in the two-dimensional integer lattice up to isomorphisms, and prove general geometric properties for those in high-dimensional cases. |
| title | On area-minimizing subgraphs in integer lattices |
| topic | Combinatorics Differential Geometry |
| url | https://arxiv.org/abs/2406.13277 |