Existence of conformal metrics with constant Q-curvature

被引：171

作者：

Djadli, Zindine ^{[1
]}

Malchiodi, Andrea ^{[2
]}

机构：

[1] Inst Fourier, Grenoble, France

[2] SISSA, I-34014 Trieste, Italy

来源：

ANNALS OF MATHEMATICS | 2008年 / 168卷 / 03期

关键词：

D O I：

10.4007/annals.2008.168.813

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a compact four dimensional manifold, we prove existence of conformal metrics with constant Q-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and min-max schemes, jointly with the compactness result of [35].

引用

页码：813 / 858

页数：46

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