Uniqueness of Complete Hypersurfaces in Weighted Riemannian Warped Products

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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Main Author: Ning Zhang
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2021/3234263
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spelling doaj-3e4a4663c061452f988fcff5af4dffff2021-07-02T17:04:55ZengHindawi LimitedAdvances 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
collection DOAJ
language English
format Article
sources DOAJ
author Ning Zhang
spellingShingle Ning Zhang
Uniqueness of Complete Hypersurfaces in Weighted Riemannian Warped Products
Advances in Mathematical Physics
author_facet Ning Zhang
author_sort Ning Zhang
title Uniqueness of Complete Hypersurfaces in Weighted Riemannian Warped Products
title_short 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_sort uniqueness of complete hypersurfaces in weighted riemannian warped products
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2021-01-01
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.
url http://dx.doi.org/10.1155/2021/3234263
work_keys_str_mv AT ningzhang uniquenessofcompletehypersurfacesinweightedriemannianwarpedproducts
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