摘要：Polyharmonic operator has found considerable interest in the literature due to its geometry roots in recent years. For instance, when $m=2$, it is the Paneitz operator, which was introduced by Paneitz \cite{paneitz} for smooth $4$ dimensional Riemannian manifoldsand and was generalized to smooth $N$ dimensional Riemannian manifolds. One can see from these papers that the problem involving polyharmonic operator presents new and challenging features in comparison with the elliptic operator (when $m=1$).In this talk, I will talk about the existence, non-existence and uniqueness for polyharmonic equation involving crtical growth.