Critical points of the Total Scalar Curvature plus Total Mean Curvature functional

被引:17
作者
Araújo, H [1 ]
机构
[1] Univ Fed Pernambuco, Dept Matemat, BR-50740540 Recife, PE, Brazil
关键词
D O I
10.1512/iumj.2003.52.2222
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The Total Scalar Curvature plus Total Mean Curvature functional is defined on the space of Riemannian metrics of a smooth compact manifold with boundary. We characterize its critical points restricted to spaces of Riemannian metrics satisfying various volume and area constraints, when the dimension of the manifold is n greater than or equal to 3. In addition, we compute the second variation of said functional at critical points and exhibit directions in which it is positive, negative or zero. These results generalize to manifolds with boundary, well known results that hold in the case of manifolds without boundary.
引用
收藏
页码:85 / 107
页数:23
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