Delaunay decompositions minimizing energy of weighted toroidal graphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866914971844083712 |
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| author | Lam, Wai Yeung |
| author_facet | Lam, Wai Yeung |
| contents | Given a weighted toroidal graph, each realization to a Euclidean torus is associated with the Dirichlet energy. By minimizing the energy over all possible Euclidean structures and over all realizations within a fixed homotopy class, one obtains a harmonic map into an optimal Euclidean torus. We show that only with this optimal Euclidean structure, the harmonic map and the edge weights are induced from a weighted Delaunay decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_03846 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Delaunay decompositions minimizing energy of weighted toroidal graphs Lam, Wai Yeung Metric Geometry Mathematical Physics Differential Geometry 52C25 Given a weighted toroidal graph, each realization to a Euclidean torus is associated with the Dirichlet energy. By minimizing the energy over all possible Euclidean structures and over all realizations within a fixed homotopy class, one obtains a harmonic map into an optimal Euclidean torus. We show that only with this optimal Euclidean structure, the harmonic map and the edge weights are induced from a weighted Delaunay decomposition. |
| title | Delaunay decompositions minimizing energy of weighted toroidal graphs |
| topic | Metric Geometry Mathematical Physics Differential Geometry 52C25 |
| url | https://arxiv.org/abs/2203.03846 |