三维规定标量曲率超曲面的内部曲率估算

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics Pub Date : 2024-05-24 DOI:10.1353/ajm.2024.a928319

Guohuan Qiu

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引用次数: 0

摘要

摘要:我们证明了在 $\mathbb{R}^{3}$ 中规定标量曲率方程的超曲面的先验内部曲率估计。该方法受 Warren 和 Yuan 的积分法启发。这里的新发现是，如果超曲面的图函数满足标量曲率方程，我们构建的 "拉格朗日 "图就是一个平均曲率有界的子曲面。

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Interior curvature estimates for hypersurfaces of prescribing scalar curvature in dimension three

abstract:

We prove a priori interior curvature estimates for hypersurfaces of prescribing scalar curvature equations in $\mathbb{R}^{3}$. The method is motivated by the integral method of Warren and Yuan. The new observation here is that we construct a ``Lagrangian'' graph which is a submanifold of bounded mean curvature if the graph function of a hypersurface satisfies a scalar curvature equation.

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来源期刊

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.