Existence of conformal metrics with constant $Q$-curvature
Analysis of PDEs
2007-05-23 v3
Abstract
Given a compact four dimensional manifold, we prove existence of conformal metrics with constant -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.
Keywords
Cite
@article{arxiv.math/0410141,
title = {Existence of conformal metrics with constant $Q$-curvature},
author = {Zindine Djadli and Andrea Malchiodi},
journal= {arXiv preprint arXiv:math/0410141},
year = {2007}
}
Comments
36 pages, revised version. To appear in Annals of Mathematics