The Bernstein problem for Sobolev intrinsic graphs in the Heisenberg group
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911122571919360 |
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| author | Golo, Sebastiano Nicolussi Cassano, Francesco Serra Vedovato, Mattia |
| author_facet | Golo, Sebastiano Nicolussi Cassano, Francesco Serra Vedovato, Mattia |
| contents | In the first Heisenberg group, we study entire, locally Sobolev intrinsic graphs that are stable for the sub-Riemannian area. We show that, under appropriate integrability conditions for the derivatives, the intrinsic graph must be an intrinsic plane, i.e., a coset of a two dimensional subgroup. This result extends \cite{arXiv:1809.04586} beyond the Lipschitz class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Bernstein problem for Sobolev intrinsic graphs in the Heisenberg group Golo, Sebastiano Nicolussi Cassano, Francesco Serra Vedovato, Mattia Differential Geometry Analysis of PDEs 53C17, 49Q20 In the first Heisenberg group, we study entire, locally Sobolev intrinsic graphs that are stable for the sub-Riemannian area. We show that, under appropriate integrability conditions for the derivatives, the intrinsic graph must be an intrinsic plane, i.e., a coset of a two dimensional subgroup. This result extends \cite{arXiv:1809.04586} beyond the Lipschitz class. |
| title | The Bernstein problem for Sobolev intrinsic graphs in the Heisenberg group |
| topic | Differential Geometry Analysis of PDEs 53C17, 49Q20 |
| url | https://arxiv.org/abs/2508.13717 |