Category: List of Bases 2007 Throughout the year RESEARCH IN MATHEMATICS

Title:

Constant Q-curvature conformal metrics in arbitrary dimension

Start Time:

14:00

Location:

ICTP (Main Building Seminar Room)

Contact:

A. Bergamo

Speaker(s):

Dr. Cheikh Birahim Ndiaye (SISSA)

Description:

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.