Constant mean curvature surfaces in the sub-Lorentzian Heisenberg group
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913173928411136 |
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| author | Borza, Samuël Pinamonti, Andrea Zoghlami, Omar |
| author_facet | Borza, Samuël Pinamonti, Andrea Zoghlami, Omar |
| contents | We study constant horizontal mean curvature surfaces in the sub-Lorentzian Heisenberg group. We derive the first-variation formula for horizontal area under volume-preserving radial variations and show that smooth isoperimetric candidates have constant horizontal mean curvature away from the characteristic set. We then give a complete classification of smooth boost-symmetric constant mean curvature surfaces: their characteristic sets, causal behaviour, and ambient sub-Lorentzian isometry classes. From this classification, we single out a family of smooth, acausal, boost-symmetric surfaces with nonzero constant mean curvature. Written as a two-sheeted graph over the exterior of a future hyperbola, this family is a natural sub-Lorentzian analogue of the Pansu bubbles and leads us to conjecture that it gives the isoperimetric maximisers in the sub-Lorentzian Heisenberg group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_31397 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Constant mean curvature surfaces in the sub-Lorentzian Heisenberg group Borza, Samuël Pinamonti, Andrea Zoghlami, Omar Differential Geometry Metric Geometry 53C50, 53C17, 53A10, 49Q05 We study constant horizontal mean curvature surfaces in the sub-Lorentzian Heisenberg group. We derive the first-variation formula for horizontal area under volume-preserving radial variations and show that smooth isoperimetric candidates have constant horizontal mean curvature away from the characteristic set. We then give a complete classification of smooth boost-symmetric constant mean curvature surfaces: their characteristic sets, causal behaviour, and ambient sub-Lorentzian isometry classes. From this classification, we single out a family of smooth, acausal, boost-symmetric surfaces with nonzero constant mean curvature. Written as a two-sheeted graph over the exterior of a future hyperbola, this family is a natural sub-Lorentzian analogue of the Pansu bubbles and leads us to conjecture that it gives the isoperimetric maximisers in the sub-Lorentzian Heisenberg group. |
| title | Constant mean curvature surfaces in the sub-Lorentzian Heisenberg group |
| topic | Differential Geometry Metric Geometry 53C50, 53C17, 53A10, 49Q05 |
| url | https://arxiv.org/abs/2605.31397 |