On Bernstein’s Problem of Complete Parabolic Hypersurfaces in Warped Products
We study constant mean curvature hypersurfaces constructed over the fiber Mn of warped products I×fMn. In this setting, assuming that the sign of the angle function does not changed along the hypersurfaces, we infer the uniqueness of such hypersurfaces by applying a parabolicity criterion. As an app...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2023-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2023/6390463 |
| _version_ | 1797790974504599552 |
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| author | Ning Zhang Zhangsheng Zhu |
| author_facet | Ning Zhang Zhangsheng Zhu |
| author_sort | Ning Zhang |
| collection | DOAJ |
| description | We study constant mean curvature hypersurfaces constructed over the fiber Mn of warped products I×fMn. In this setting, assuming that the sign of the angle function does not changed along the hypersurfaces, we infer the uniqueness of such hypersurfaces by applying a parabolicity criterion. As an application, we get some Bernstein type theorems. |
| first_indexed | 2024-03-13T02:12:09Z |
| format | Article |
| id | doaj.art-85fa63cd41d74377a388a95cce7c2087 |
| institution | Directory Open Access Journal |
| issn | 1687-9139 |
| language | English |
| last_indexed | 2024-03-13T02:12:09Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj.art-85fa63cd41d74377a388a95cce7c20872023-07-01T00:00:29ZengHindawi LimitedAdvances in Mathematical Physics1687-91392023-01-01202310.1155/2023/6390463On Bernstein’s Problem of Complete Parabolic Hypersurfaces in Warped ProductsNing Zhang0Zhangsheng Zhu1School of ScienceSchool of ScienceWe study constant mean curvature hypersurfaces constructed over the fiber Mn of warped products I×fMn. In this setting, assuming that the sign of the angle function does not changed along the hypersurfaces, we infer the uniqueness of such hypersurfaces by applying a parabolicity criterion. As an application, we get some Bernstein type theorems.http://dx.doi.org/10.1155/2023/6390463 |
| spellingShingle | Ning Zhang Zhangsheng Zhu On Bernstein’s Problem of Complete Parabolic Hypersurfaces in Warped Products Advances in Mathematical Physics |
| title | On Bernstein’s Problem of Complete Parabolic Hypersurfaces in Warped Products |
| title_full | On Bernstein’s Problem of Complete Parabolic Hypersurfaces in Warped Products |
| title_fullStr | On Bernstein’s Problem of Complete Parabolic Hypersurfaces in Warped Products |
| title_full_unstemmed | On Bernstein’s Problem of Complete Parabolic Hypersurfaces in Warped Products |
| title_short | On Bernstein’s Problem of Complete Parabolic Hypersurfaces in Warped Products |
| title_sort | on bernstein s problem of complete parabolic hypersurfaces in warped products |
| url | http://dx.doi.org/10.1155/2023/6390463 |
| work_keys_str_mv | AT ningzhang onbernsteinsproblemofcompleteparabolichypersurfacesinwarpedproducts AT zhangshengzhu onbernsteinsproblemofcompleteparabolichypersurfacesinwarpedproducts |