Existence of conformal metrics with constant Q-curvature

2004/10/06 by Zindine Djadli, Djadli, Zindine, Andrea Malchiodi +1 · 3 citations
Mathematics · #35B33 #35J35 #53A30 #53C21 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B33 #msc:35J35 #msc:53A30 #msc:53C21

paper · pdf · doi:10.48550/arxiv.math/0410141

36 pages, revised version. To appear in Annals of Mathematics

arxiv created 2006/04/18 · arxiv updated 2009/12/01

Abstract

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 minimax schemes, jointly with a compactness result by the second author.

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