This is the second paper of a series of three on the regularity of higher
codimension area minimizing integral currents. Here we perform the second main
step in the analysis of the singularities, namely the construction of a center
manifold, i.e. an approximate average of the sheets of an almost flat area
minimizing current. Such center manifold is complemented with a Lipschitz
multi-valued map on its normal bundle, which approximates the current with a
highe degree of accuracy. In the third and final paper these objects are used
to conclude a new proof of Almgren's celebrated dimension bound on the singular
set.Comment: In the new version the proofs and the structure are improved and some
minor errors have been correcte
