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.

引用

页数：30

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