The Yamabe problem is to look for a metric with constant
scalar curvature in each conformal class of metrics. The equivalent
equation is a semilinear equation. In our talk, we will use Schouten
tensor $A:=Ricci-(R/2(n-1))g$ to generalize the Yamabe problem to a
problem and the equivalent equation is a fully nonlinear elliptic
equation. We will consider the generalized problem on compact manifolds
with/without boundaries.