9/28/2007

Cheikh Ndiaye
SISSA, Italy

Constant Q-curvature conformal metrics in arbitrary dimensions

In this talk, we will discuss the problem of finding metrics with constant Q-curvature on a given closed Riemannian manifold (M,g) with dimension an arbitrary integer n≥3. This will be equivalent to solving an n-th order elliptic PDE (if n is even) or an n-th order integral equation (if n is odd) with exponential nonlinearity and variational structure in both cases. However when the total integral of the Q-curvature is large, the Euler-Lagrange functional associated is unbounded from below, implying that we have to find critical points of saddle type. Using a min-max scheme whose construction is based on concentration of volume, we solve the problem under general assumptions which are also conformally invariant.