A COMPACTNESS THEOREM ON BRANSON'S Q-CURVATURE EQUATION

被引：9

作者：

Li, Gang ^{[1
,2
]}

机构：

[1] Peking Univ, Beijing Int Ctr Math Res, Beijing, Peoples R China

[2] Shandong Univ, Dept Math, Jian, Jiangxi, Peoples R China

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2019年 / 302卷 / 01期

基金：

中国博士后科学基金;

关键词：

compactness; constant Q-curvature metrics; blowup argument; positive mass theorem; maximum principle; fourth order elliptic equations; BLOW-UP PHENOMENA; YAMABE PROBLEM; CONFORMAL METRICS; SCALAR CURVATURE; PANEITZ EQUATION; INVARIANT; OPERATORS; PROOF;

D O I：

10.2140/pjm.2019.302.119

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (M, g) be a closed Riemannian manifold of dimension 5 <= n <= 7. Assume that (M, g) is not conformally equivalent to the round sphere. If the scalar curvature R-g is greater than or equal to 0 and the Q-curvature Q(g) is greater than or equal to 0 on M with Q(g)(p) > 0 for some point p is an element of M, we prove that the set of metrics in the conformal class of g with prescribed constant positive Q-curvature is compact in C-4,C- alpha for any 0 < alpha < 1.

引用

页码：119 / 179

页数：61

共 40 条

[1]

ARMITAGE DH, 1973, J LOND MATH SOC, V7, P251

[2] DIFFERENTIAL-OPERATORS CANONICALLY ASSOCIATED TO A CONFORMAL STRUCTURE [J].

BRANSON, TP .

MATHEMATICA SCANDINAVICA, 1985, 57 (02) :293-345

[3]

Brendle S, 2008, J AM MATH SOC, V21, P951

[4]

Brendle S, 2009, J DIFFER GEOM, V81, P225

[5] On a class of locally conformally flat manifolds [J].

Chang, SYA ;

Hang, FB ;

Yang, PC .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2004, 2004 (04) :185-209

[6]

Chen CC, 1998, J DIFFER GEOM, V49, P115

[7] Nonlinear biharmonic equations with negative exponents [J].

Choi, Y. S. ;

Xu, Xingwang .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (01) :216-234

[8]

Djadli Z, 2000, DUKE MATH J, V104, P129

[9]

Druet O, 2004, INT MATH RES NOTICES, V2004, P1143

[10]

EICHMAIR M, 2013, COMMUN MATH PHYS, V319, P575

← 1 2 3 4 →