Constant Q-curvature conformal metrics in arbitrary dimension
ICTP (Main Building Seminar Room)
Dr. Cheikh Birahim Ndiaye
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 elliptic 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 point 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.
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