  We derive the analogue of the vanishing of the cosmological constant in 3+1
dimensions, T_0^0 = 0, in terms of an integral over components of the
energy-momentum tensor of a 4+1 dimensional universe with parallel
three-branes, and an additional constraint local to the branes. The basic
ingredients are the existence of a static solution of the Einstein equations,
and the compactness of the 5th dimension. The corresponding constraints are
applied to a general action of scalar fields with arbitrary potentials in the
bulk and on the branes. The equations of motion are solved in a linearized
approximation in the 5th dimension, whereupon they require the search for
extrema of an ``effective potential'', which depends nonlinearly on the action
in the bulk and on the branes. The previous constraints then turn into the
vanishing of this ``effective potential'' at the extremum.
