Uniqueness of Complete Hypersurfaces in Weighted Riemannian Warped Products
In this paper, applying the weak maximum principle, we obtain the uniqueness results for the hypersurfaces under suitable geometric restrictions on the weighted mean curvature immersed in a weighted Riemannian warped product I×ρMfn whose fiber M has f-parabolic universal covering. Furthermore, appli...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/3234263 |
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| author | Ning Zhang |
| author_facet | Ning Zhang |
| author_sort | Ning Zhang |
| collection | DOAJ |
| description | In this paper, applying the weak maximum principle, we obtain the uniqueness results for the hypersurfaces under suitable geometric restrictions on the weighted mean curvature immersed in a weighted Riemannian warped product I×ρMfn whose fiber M has f-parabolic universal covering. Furthermore, applications to the weighted hyperbolic space are given. In particular, we also study the special case when the ambient space is weighted product space and provide some results by Bochner’s formula. As a consequence of this parametric study, we also establish Bernstein-type properties of the entire graphs in weighted Riemannian warped products. |
| format | Article |
| id | doaj-art-3e4a4663c061452f988fcff5af4dffff |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-3e4a4663c061452f988fcff5af4dffff2025-02-03T01:28:31ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/32342633234263Uniqueness of Complete Hypersurfaces in Weighted Riemannian Warped ProductsNing Zhang0School of Science, Henan Institute of Technology, Xinxiang 453003, ChinaIn this paper, applying the weak maximum principle, we obtain the uniqueness results for the hypersurfaces under suitable geometric restrictions on the weighted mean curvature immersed in a weighted Riemannian warped product I×ρMfn whose fiber M has f-parabolic universal covering. Furthermore, applications to the weighted hyperbolic space are given. In particular, we also study the special case when the ambient space is weighted product space and provide some results by Bochner’s formula. As a consequence of this parametric study, we also establish Bernstein-type properties of the entire graphs in weighted Riemannian warped products.http://dx.doi.org/10.1155/2021/3234263 |
| spellingShingle | Ning Zhang Uniqueness of Complete Hypersurfaces in Weighted Riemannian Warped Products Advances in Mathematical Physics |
| title | Uniqueness of Complete Hypersurfaces in Weighted Riemannian Warped Products |
| title_full | Uniqueness of Complete Hypersurfaces in Weighted Riemannian Warped Products |
| title_fullStr | Uniqueness of Complete Hypersurfaces in Weighted Riemannian Warped Products |
| title_full_unstemmed | Uniqueness of Complete Hypersurfaces in Weighted Riemannian Warped Products |
| title_short | Uniqueness of Complete Hypersurfaces in Weighted Riemannian Warped Products |
| title_sort | uniqueness of complete hypersurfaces in weighted riemannian warped products |
| url | http://dx.doi.org/10.1155/2021/3234263 |
| work_keys_str_mv | AT ningzhang uniquenessofcompletehypersurfacesinweightedriemannianwarpedproducts |