## Conformal metrics with constant $Q$-curvature

### Summary

Summary: 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.

### Mathematics Subject Classification

35B33, 35J35, 53A30, 53C21

### Keywords/Phrases

$Q$-curvature, geometric pdes, variational methods, MIN-MAX schemes