Fourth-order uniformization type theorems for 4-dimensional Riemannian manifolds

• Applicants: Professor Dr. Mohameden Ould Ahmedou; Professor Dr. Reiner Schätzle
• Subject Area: Mathematics
• Term: from 2013 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 231560147

For a given compact Riemannian manifold, the Q-curvature is a scalar quantity, which turns out to be of crucial importance for the understanding of the geometry and topology of four-dimensional compact Riemannian manifolds. The main goal of this project is to establish new fourth- order uniformization type theorems for four-dimensional compact Riemannian manifold without and with boundary.Precisely, we plan to prove new existence results for the problem of existence of conformal metrics with constant (resp. prescribed) Q-curvature on four-dimensional compact Riemannian manifold without and with boundary in the critical case.

• DFG Programme: Research Grants