On the $\sigma_2$scalar curvature and its application
On the $\sigma_2$scalar curvature and its application

Yuxin Ge, Université ParisEst Créteil  UPEC
Fine Hall 314
In this talk, we establish an analytic foundation for a fully nonlinear equation $\frac{\sigma_2}{\sigma_1}=f$ on manifolds with positive scalar curvature. This equation arises from conformal geometry. As application, we prove that, if a compact 3dimensional manifold $M$ admits a riemannian metric with positive scalar curvature and $\int \sigma_2\ge 0$, then topologically $M$ is a quotient of sphere.