  We prove that every Weil-Petersson isometry of the Teichmuller space T(g,n)
is induced by an element of the extended mapping class group; here 3g-3+n > 1
and (g,n) is not (1,2). Our method follows Ivanov's proof of the Royden's
analogous theorem for the Teichmuller metric: we study the action of an
isometry on the frontier of the metric completion of the Teichmuller space, and
show that the isometry then induces an automorphism on the relevant complex of
curves. Some synthetic geometry of the Weil-Petersson metric completes the
proof.
