  We prove a generalization of the Ahlswede-Cai local-global principle. A new
technique to handle edge-isoperimetric problems is introduced which we call the
pull-push method. Our main result includes all previously published results in
this area as special cases with the only exception of the edge-isoperimetric
problem for grids. With this we partially answer a question of Harper on
local-global principles. We also describe a strategy for further generalization
of our results so that the case of grids would be covered, which would
completely settle Harper's question.
