ON THE STABILITY OF COMPACTIFIED D=11 SUPERMEMBRANES - GLOBAL ASPECTSOF THE BOSONIC SECTOR

We prove that the Hamiltonian for the bosonic sector of D = 11 superme mbrane theories, wrapped in an irreducible way around S-1 x S-1 x M-9 on the target manifold, only has strict minima without infinite-dimens ional valleys. The minima occur at monopole connections of an associat ed U(1) bundle over topologically non-trivial Riemann surfaces of arbi trary genus. Explicit expressions for the minimal connections in terms of membrane maps are presented. (C) 1998 Elsevier Science B.V.