Compactness for conformal scalar-flat metrics on umbilic boundary manifolds

被引：8
|
作者：
Ghimenti, Marco [1 ]
Micheletti, Anna Maria [1 ]
机构：
[1] Univ Pisa, Dipartimento Matemat, Largo B Pontecorvo 5, Pisa, Italy
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 200卷 / 200期
关键词：
Scalar flat metrics; Umbilic boundary; Yamabe problem; Compactness; BLOW-UP PHENOMENA; YAMABE PROBLEM; EXISTENCE THEOREM; CONSTANT; DEFORMATION; CURVATURE; EQUATIONS;
D O I：
10.1016/j.na.2020.111992
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let (M, g) a compact Riemannian n-dimensional manifold with umbilic boundary. It is well known that, under certain hypothesis, in the conformal class of g there are scalar-flat metrics that have partial derivative M as a constant mean curvature hypersurface. In this paper we prove that these metrics are a compact set, provided n = 8 and the Weyl tensor of the boundary is always different from zero, or if n > 8 and the Weyl tensor of M is always different from zero on the boundary. (C) 2020 Elsevier Ltd. All rights reserved.
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页数：30
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