The Han-Li conjecture in constant scalar curvature and constant boundary mean curvature problem on compact manifolds

被引：12

作者：

Chen, Xuezhang ^{[1
,2
]}

Ruan, Yuping ^{[1
,2
,4
]}

Sun, Liming ^{[3
]}

机构：

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

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

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

[4] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

ADVANCES IN MATHEMATICS | 2019年 / 358卷

基金：

中国国家自然科学基金;

关键词：

Mountain Pass Lemma; Conformal Fermi coordinates; Boundary Yamabe problem; Positive mass theorem; YAMABE PROBLEM; FLAT METRICS; CONFORMAL DEFORMATION; UNIQUENESS THEOREMS; EXISTENCE THEOREM; CONVERGENCE; FLOWS;

D O I：

10.1016/j.aim.2019.106854

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Han-Li conjecture states that: Let (M, go) be an ndimensional (n >= 3) smooth compact Riemannian manifold with boundary having positive (generalized) Yamabe constant and c be any real number, then there exists a conformal metric of g(0) with scalar curvature 1 and boundary mean curvature c. Combining with Z.C. Han and Y.Y. Li's results, we answer this conjecture affirmatively except for the case that n >= 8, the boundary is umbilic, the Weyl tensor of M vanishes on the boundary and has an interior non-zero point. (C) 2019 Elsevier Inc. All rights reserved.

引用

页数：56

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