  We prove D=11 supermembrane theories wrapping around in an irreducible way
over $S^{1} \times S^{1}\times M^{9}$ on the target manifold, have a
hamiltonian with strict minima and without infinite dimensional valleys at the
minima for the bosonic sector. The minima occur at monopole connections of an
associated U(1) bundle over topologically non trivial Riemann surfaces of
arbitrary genus. Explicit expressions for the minimal connections in terms of
membrane maps are presented. The minimal maps and corresponding connections
satisfy the BPS condition with half SUSY.
