Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 120, 11 pages      arXiv:0712.2123      https://doi.org/10.3842/SIGMA.2007.120
Contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson

Conformal Metrics with Constant Q-Curvature

Andrea Malchiodi
SISSA, Via Beirut 2-4, Trieste, Italy

Received September 02, 2007, in final form December 05, 2007; Published online December 13, 2007

Abstract
We consider the problem of varying conformally the metric of a four dimensional manifold in order to obtain constant Q-curvature. The problem is variational, and solutions are in general found as critical points of saddle type. We show how the problem leads naturally to consider the set of formal barycenters of the manifold.

Key words: Q-curvature; geometric PDEs; variational methods; min-max schemes.

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