Exact solutions for U(1) globally invariant membranes

The exact solvability problem of the nonlinear equations describing the U(1) invariant membranes is studied and the general solution for the static membrane in D=(2N+1)-dimensional Minkowski space-time, including M-theory case D=11, is obtained. The D=5 time-dependent elliptic cosine solution describing a family of contracting tori is also found, together with the solution corresponding to a spinning torus characterized by the presence of the critical rotation frequency Ωmax=T1/3π expressed via the membrane tension T.