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Compactness for conformal scalar-flat metrics on umbilic boundary manifolds
Nonlinear Analysis ( IF 1.4 ) Pub Date : 2020-05-26 , DOI: 10.1016/j.na.2020.111992 Marco Ghimenti , Anna Maria Micheletti
中文翻译:
脐边界流形上共形标量-平坦度量的紧度
更新日期:2020-05-26
Nonlinear Analysis ( IF 1.4 ) Pub Date : 2020-05-26 , DOI: 10.1016/j.na.2020.111992 Marco Ghimenti , Anna Maria Micheletti
Let a compact Riemannian -dimensional manifold with umbilic boundary. It is well known that, under certain hypothesis, in the conformal class of there are scalar-flat metrics that have as a constant mean curvature hypersurface. In this paper we prove that these metrics are a compact set, provided and the Weyl tensor of the boundary is always different from zero, or if and the Weyl tensor of is always different from zero on the boundary.
中文翻译:
脐边界流形上共形标量-平坦度量的紧度
让 紧凑的黎曼方程 脐边界的三维流形。众所周知,在某些假设下, 有标量平指标 作为恒定的平均曲率超曲面。在本文中,我们证明了这些指标是一个紧凑集合,只要 并且边界的Weyl张量始终不为零,或者 和的Weyl张量 在边界上总是不同于零。