Existence of conformal metrics with constant Q-curvature

• 成果类型: Article
• 署名作者: Djadli, Zindine; Malchiodi, Andrea
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2008.168.813
• 发表日期: 2008
• 页码: 813-858
• 关键词: zeta-function determinants; invariant; equation; 4-manifolds; INEQUALITY; exponent; FLOW

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].