标量曲率纤维上的巴特尼克希尔伯特流形结构和约束算子

IF 0.7 4区数学 Q2 MATHEMATICS

Communications in Analysis and Geometry Pub Date : 2024-07-16 DOI:10.4310/cag.2023.v31.n5.a8

Delay,Erwann

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引用次数: 0

摘要

我们采用巴特尼克方法，为任意维度 $\geq 3$ 的紧凑流形上的真空约束方程的解空间提供了一个不含 KID 的希尔伯特流形结构。在课程中，我们证明了标量曲率或约束算子的一些纤维是希尔伯特子流形。我们还研究了与 KID 算子相关的一些算子和不等式。最后，我们对一些非紧凑流形的适应性进行了评论。

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Bartnik Hilbert manifold structure on fibers of the scalar curvature and the constraint operator

We adapt the Bartnik method to provide a Hilbert manifold structure for the space of solutions, without KID's, to the vacuum constraint equations on compact manifold of any dimension $\geq 3$. In the course, we prove that some fibers of the scalar curvature or the constraint operator are Hilbert submanifolds. We also study some operators and inequalities related to the KID's operator. Finally we comment the adaptation to some non-compact manifolds.

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来源期刊

Communications in Analysis and Geometry 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high-quality papers on subjects related to classical analysis, partial differential equations, algebraic geometry, differential geometry, and topology.