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

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Advances in Mathematical Physics Pub Date : 2023-06-23 DOI:10.1155/2023/6390463

Ning Zhang, Zhangsheng Zhu

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引用次数: 0

Abstract

We study constant mean curvature hypersurfaces constructed over the fiber

M^{n}

of warped products

I \times_{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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关于弯曲积中完全抛物超曲面的Bernstein问题

我们研究了在弯曲产物I ×的纤维mn上构造的常平均曲率超曲面f M n。在这种情况下，假设角度函数的符号沿着超曲面不改变，我们通过应用抛物线性准则来推断这种超曲面的唯一性。作为应用，我们得到了一些Bernstein型定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Mathematical Physics 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

151

审稿时长

>12 weeks

期刊介绍： Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.