Existence of conformal metrics with constant scalar curvature and constant boundary mean curvature on compact manifolds

被引：7

作者：

Chen, Xuezhang ^{[1
,2
]}

Sun, Liming ^{[3
,4
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

[2] Nanjing Univ, IMS, Nanjing 210093, Jiangsu, Peoples R China

[3] Rutgers State Univ, Dept Math, 110 Frenlinghuysen Rd, Piscataway, NJ 08854 USA

[4] Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2019年 / 21卷 / 03期

关键词：

Scalar curvature; mean curvature; manifold with boundary; critical exponent; positive conformal invariant; YAMABE PROBLEM; FLAT METRICS; UNIQUENESS THEOREMS; ELLIPTIC-EQUATIONS; DEFORMATION; CONVERGENCE; FLOW;

D O I：

10.1142/S0219199718500219

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the problem of deforming a Riemannian metric to a conformal one with nonzero constant scalar curvature and nonzero constant boundary mean curvature on a compact manifold of dimension n >= 3. We prove the existence of such conformal metrics in the cases of n = 6, 7 or the manifold is spin and some other remaining ones left by Escobar. Furthermore, in the positive Yamabe constant case, by normalizing the scalar curvature to be 1, there exists a sequence of conformal metrics such that their constant boundary mean curvatures go to +infinity.

引用

页数：51

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