Minimal horizontal triods: Analysis and computation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908851471646720 |
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| author | Nürnberg, Robert Pozzi, Paola |
| author_facet | Nürnberg, Robert Pozzi, Paola |
| contents | In this article we investigate the question of finding a network configuration of minimal length connecting three given points in the Heisenberg group. After proving existence of (possibly degenerate) minimal horizontal triods, we investigate their characterization. We then formulate a horizontal curve shortening flow that deforms any given suitable initial triod into a critical point for the length functional. Numerical experiments based on a stable fully discrete finite element scheme provide useful insights into the rich landscape of this sub-Riemannian geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15740 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal horizontal triods: Analysis and computation Nürnberg, Robert Pozzi, Paola Analysis of PDEs Numerical Analysis Differential Geometry In this article we investigate the question of finding a network configuration of minimal length connecting three given points in the Heisenberg group. After proving existence of (possibly degenerate) minimal horizontal triods, we investigate their characterization. We then formulate a horizontal curve shortening flow that deforms any given suitable initial triod into a critical point for the length functional. Numerical experiments based on a stable fully discrete finite element scheme provide useful insights into the rich landscape of this sub-Riemannian geometry. |
| title | Minimal horizontal triods: Analysis and computation |
| topic | Analysis of PDEs Numerical Analysis Differential Geometry |
| url | https://arxiv.org/abs/2507.15740 |