Existence and uniqueness of $t$-graphs of prescribed mean curvature in Heisenberg groups
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910442385833984 |
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| author | Pozuelo, Julián Verzellesi, Simone |
| author_facet | Pozuelo, Julián Verzellesi, Simone |
| contents | We study the prescribed mean curvature equation for $t$-graphs in a Riemannian Heisenberg group of arbitrary dimension. We characterize the existence of classical solutions in a bounded domain without imposing Dirichlet boundary data, and we provide conditions that guarantee uniqueness. Moreover, we extend previous results to solve the Dirichlet problem when the mean curvature is non-constant. Finally, by an approximation technique, we obtain solutions to the sub-Riemannian prescribed mean curvature equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06533 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and uniqueness of $t$-graphs of prescribed mean curvature in Heisenberg groups Pozuelo, Julián Verzellesi, Simone Differential Geometry Analysis of PDEs 53C17, 49Q10, 53A10 We study the prescribed mean curvature equation for $t$-graphs in a Riemannian Heisenberg group of arbitrary dimension. We characterize the existence of classical solutions in a bounded domain without imposing Dirichlet boundary data, and we provide conditions that guarantee uniqueness. Moreover, we extend previous results to solve the Dirichlet problem when the mean curvature is non-constant. Finally, by an approximation technique, we obtain solutions to the sub-Riemannian prescribed mean curvature equation. |
| title | Existence and uniqueness of $t$-graphs of prescribed mean curvature in Heisenberg groups |
| topic | Differential Geometry Analysis of PDEs 53C17, 49Q10, 53A10 |
| url | https://arxiv.org/abs/2405.06533 |