A COMPACTNESS THEOREM FOR THE YAMABE PROBLEM

被引：0

作者：

Khuri, M. A. ^{[1
]}

Marques, F. C. ^{[2
]}

Schoen, R. M. ^{[3
]}

机构：

[1] SUNY Stony Brook, Stony Brook, NY 11794 USA

[2] IMPA, BR-22460320 Rio De Janeiro, Brazil

[3] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

JOURNAL OF DIFFERENTIAL GEOMETRY | 2009年 / 81卷 / 01期

关键词：

SCALAR CURVATURE; EQUATIONS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove compactness for the full set of solutions to the Yamabe Problem if n <= 24. After proving sharp pointwise estimates at a blowup point, we prove the Weyl Vanishing Theorem in those dimensions, and reduce the compactness question to showing positivity of a quadratic form. We also show that this quadratic form has negative eigenvalues if n >= 25.

引用

页码：143 / 196

页数：54

共 50 条

[41] Aubin's Lemma for the Yamabe constants of infinite coverings and a positive mass theorem [J].

Akutagawa, Kazuo .

MATHEMATISCHE ANNALEN, 2012, 352 (04) :829-864

[42] A COMPACTNESS THEOREM ON BRANSON'S Q-CURVATURE EQUATION [J].

Li, Gang .

PACIFIC JOURNAL OF MATHEMATICS, 2019, 302 (01) :119-179

[43] Critical point theorem for asymptotically quadratic functional without compactness [J].

Liang, Zhanping ;

Su, Jiabao .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 370 (02) :649-658

[44] The zero scalar curvature Yamabe problem on noncompact manifolds with boundary [J].

Schwartz, Fernando .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2006, 55 (04) :1449-1459

[45] On the problem of prescribing weighted scalar curvature and the weighted Yamabe flow [J].

Ho, Pak Tung ;

Shin, Jinwoo .

ANALYSIS AND GEOMETRY IN METRIC SPACES, 2023, 11 (01)

[46] Harmonically free group actions and equivariant bifurcation in the Yamabe problem [J].

Moreira, Ana Claudia .

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2018, 56 :234-259

[47] On the Yamabe problem and the scalar curvature problems under boundary conditions [J].

Antonio Ambrosetti ;

YanYan Li ;

Andrea Malchiodi .

Mathematische Annalen, 2002, 322 :667-699

[48] Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem [J].

不详 .

MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 231 (1086) :1-+

[49] An analytic construction of singular solutions related to a critical Yamabe problem [J].

Chan, Hardy ;

DelaTorre, Azahara .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2020, 45 (11) :1621-1646

[50] The Asymptotically Flat Scalar-Flat Yamabe Problem with Boundary [J].

McCormick, Stephen .

JOURNAL OF GEOMETRIC ANALYSIS, 2017, 27 (03) :2269-2277

← 1 2 3 4 5 →