The prescribed mean curvature equation for $t$-graphs in the sub-Finsler Heisenberg group $\mathbb{H}^n$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866929370172489728 |
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| author | Giovannardi, Gianmarco Pinamonti, Andrea Pozuelo, Julián Verzellesi, Simone |
| author_facet | Giovannardi, Gianmarco Pinamonti, Andrea Pozuelo, Julián Verzellesi, Simone |
| contents | We study the sub-Finsler prescribed mean curvature equation, associated to a strictly convex body $K_0 \subseteq \mathbb{R}^{2n}$, for $t$-graphs on a bounded domain $Ω$ in the Heisenberg group $\mathbb{H}^n$. When the prescribed datum $H$ is constant and strictly smaller that the Finsler mean curvature of $\partial Ω$, we prove the existence of a Lipschitz solution to the Dirichlet problem for the sub-Finsler CMC equation by means of a Finsler approximation scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_13414 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The prescribed mean curvature equation for $t$-graphs in the sub-Finsler Heisenberg group $\mathbb{H}^n$ Giovannardi, Gianmarco Pinamonti, Andrea Pozuelo, Julián Verzellesi, Simone Analysis of PDEs Differential Geometry 53C17, 49Q10, 53A10 We study the sub-Finsler prescribed mean curvature equation, associated to a strictly convex body $K_0 \subseteq \mathbb{R}^{2n}$, for $t$-graphs on a bounded domain $Ω$ in the Heisenberg group $\mathbb{H}^n$. When the prescribed datum $H$ is constant and strictly smaller that the Finsler mean curvature of $\partial Ω$, we prove the existence of a Lipschitz solution to the Dirichlet problem for the sub-Finsler CMC equation by means of a Finsler approximation scheme. |
| title | The prescribed mean curvature equation for $t$-graphs in the sub-Finsler Heisenberg group $\mathbb{H}^n$ |
| topic | Analysis of PDEs Differential Geometry 53C17, 49Q10, 53A10 |
| url | https://arxiv.org/abs/2207.13414 |