On the Steiner tree connecting a fractal set
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929719544381440 |
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| author | Paolini, Emanuele Stepanov, Eugene |
| author_facet | Paolini, Emanuele Stepanov, Eugene |
| contents | We construct an example of an infinite planar embedded self-similar binary tree $Σ$ which is the essentially unique solution to the Steiner problem of finding the shortest connection of a given planar self-similar fractal set $C$ of positive Hausdorff dimension. The set $C$ can be considered the set of leaves, or the ``boundary``, of the tree $Σ$, so that $Σ$ is an irreducible solution to the Steiner problem with datum $C$ (i.e. $Σ\setminus C$ is connected). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01932 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Steiner tree connecting a fractal set Paolini, Emanuele Stepanov, Eugene Metric Geometry Differential Geometry Optimization and Control Primary 49Q20, 49Q05, 49Q10. Secondary 05C63 We construct an example of an infinite planar embedded self-similar binary tree $Σ$ which is the essentially unique solution to the Steiner problem of finding the shortest connection of a given planar self-similar fractal set $C$ of positive Hausdorff dimension. The set $C$ can be considered the set of leaves, or the ``boundary``, of the tree $Σ$, so that $Σ$ is an irreducible solution to the Steiner problem with datum $C$ (i.e. $Σ\setminus C$ is connected). |
| title | On the Steiner tree connecting a fractal set |
| topic | Metric Geometry Differential Geometry Optimization and Control Primary 49Q20, 49Q05, 49Q10. Secondary 05C63 |
| url | https://arxiv.org/abs/2304.01932 |