  It was proved by Graham and Witten in 1999 that conformal invariants of
submanifolds can be obtained via volume renormalization of minimal surfaces in
conformally compact Einstein manifolds. The conformal invariant of a
submanifold $\Sigma$ is contained in the volume expansion of the minimal
surface which is asymptotic to $\Sigma$ when the minimal surface approaches the
conformaly infinity. In the paper we give the explicit expression of
Graham-Witten's conformal invariant for closed four dimensional submanifolds
and find critical points of the conformal invariant in the case of Euclidean
ambient spaces.
