A Moser-Bernstein problem for Riemannian warped products
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929236163428352 |
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| author | Albujer, Alma L. Herrera, Jónatan Rubio, Rafael M. |
| author_facet | Albujer, Alma L. Herrera, Jónatan Rubio, Rafael M. |
| contents | In this work we deal with an elliptic non-linear problem, which arises naturally from Riemannian geometry. This problem has clasically been studied in the the Euclidean $n$-dimensional space and it is known as the Moser-Bernstein problem. Nevertheless we solve this type of problems in a wide family of Riemannian manifolds, constructed as Riemannian warped products. More precicely, we study the entire solutions to the minimal hypersurface equation in a Riemannian warped product $M=P\times_h\mathbb{R}$, where $P$ is a complete Riemannian parabolic manifold and $h$ a positive smooth function on $P$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_04455 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Moser-Bernstein problem for Riemannian warped products Albujer, Alma L. Herrera, Jónatan Rubio, Rafael M. Differential Geometry Mathematical Physics 35J93, 58J05, 53C42, 53A10 In this work we deal with an elliptic non-linear problem, which arises naturally from Riemannian geometry. This problem has clasically been studied in the the Euclidean $n$-dimensional space and it is known as the Moser-Bernstein problem. Nevertheless we solve this type of problems in a wide family of Riemannian manifolds, constructed as Riemannian warped products. More precicely, we study the entire solutions to the minimal hypersurface equation in a Riemannian warped product $M=P\times_h\mathbb{R}$, where $P$ is a complete Riemannian parabolic manifold and $h$ a positive smooth function on $P$. |
| title | A Moser-Bernstein problem for Riemannian warped products |
| topic | Differential Geometry Mathematical Physics 35J93, 58J05, 53C42, 53A10 |
| url | https://arxiv.org/abs/2402.04455 |