Rigidity of hypersurfaces and Moser–Bernstein type results in certain warped products, with applications to pseudo-hyperbolic spaces

Araújo, Jogli G.; Lima, Henrique F. de; Gomes, Wallace F.

doi:10.1007/s00010-022-00914-1

Cited by 3 publications

(1 citation statement)

References 26 publications

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“…It should also be noticed that the similar idea has been used to obtain the rigidity of hypersurfaces in warped products (see [10], Theorem 4.11). Nevertheless, we take a different approach to prove our main uniqueness results (Theorems 2 and 4) of constant mean curvature hypersurfaces in warped products.…”

Section: Parametric Uniqueness Resultsmentioning

confidence: 99%

On Bernstein’s Problem of Complete Parabolic Hypersurfaces in Warped Products

Zhang

Zhu

2023

Advances in Mathematical Physics

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We study constant mean curvature hypersurfaces constructed over the fiber M n of warped products I × f M n . 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.

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Section: Parametric Uniqueness Resultsmentioning

confidence: 99%

On Bernstein’s Problem of Complete Parabolic Hypersurfaces in Warped Products

Zhang

Zhu

2023

Advances in Mathematical Physics

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Uniqueness of Complete Hypersurfaces

Fernandes de Lima,

Molica Bisci,

Velásquez

2024

Frontiers in Mathematics

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Nonexistence of mean curvature flow solitons with polynomial volume growth immersed in certain semi-Riemannian warped products

Batista,

Molica Bisci,

de Lima

et al. 2024

Advances in Nonlinear Analysis

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Our purpose is to establish nonexistence results concerning complete noncompact mean curvature flow solitons with polynomial volume growth immersed in certain semi-Riemannian warped products, under mild constraints on the warping and soliton functions. Applications to self-shrinkers in the Euclidean space, as well as to mean curvature flow solitons in other important warped product models such as the Schwarzschild and Reissner-Nordström spaces, and Robertson-Walker spacetimes such as the Einstein-de Sitter spacetime, are also given. Furthermore, we study the nonexistence of entire solutions to the mean curvature flow equation. Our approach is based on a suitable conformal change of metric jointly with a maximum principle for complete noncompact Riemannian manifolds with polynomial volume growth due to Alías et al.

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Rigidity of hypersurfaces and Moser–Bernstein type results in certain warped products, with applications to pseudo-hyperbolic spaces

Cited by 3 publications

References 26 publications

On Bernstein’s Problem of Complete Parabolic Hypersurfaces in Warped Products

On Bernstein’s Problem of Complete Parabolic Hypersurfaces in Warped Products

Uniqueness of Complete Hypersurfaces

Nonexistence of mean curvature flow solitons with polynomial volume growth immersed in certain semi-Riemannian warped products

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