论文标题
标量曲率和约束操作员的纤维上的Bartnik Hilbert歧管结构
Bartnik Hilbert manifold structure on fibers of the scalar curvature and the constraint operator
论文作者
论文摘要
我们将Bartnik方法调整为在没有孩子的情况下为解决方案空间提供Hilbert歧管结构，以在任何维度$ \ geq 3 $的紧凑型歧管上的真空约束方程。在本课程中，我们证明标量曲率或约束操作员的某些纤维是希尔伯特·苏布曼福德（Hilbert submanifolds）。我们还研究了一些与儿童操作员有关的操作员和不平等现象。最后，我们评论了对某些非紧凑型歧管的改编。
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.
