  In the work by T. Duyckaerts and F. Merle, they studied the variational
structure near the ground state solution $W$ of the energy critical wave
equation and classified the solutions with the threshold energy $E(W,0)$ in
dimensions $d=3,4,5$. In this paper, we extend the results to all dimensions
$d\ge 6$. The main issue in high dimensions is the non-Lipschitz continuity of
the nonlinearity which we get around by making full use of the decay property
of $W$.
