Conformal Metrics with Constant Q-Curvature

Details Conformal Metrics with Constant Q-Curvature Conformal Metrics with Constant Q-Curvature

2007-12-13

arxiv.org/abs/0712.2123v1

SIGMA 3 (2007), 120, 11 pages

Mathematics

Differential Geometry

This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in

Scientific paper

10.3842/SIGMA.2007.120

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.

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