  We consider variational properties of some numerical invariants, measuring
convergence of local horizontal sections, associated to differential modules on
polyannuli over a nonarchimedean field of characteristic zero. This extends
prior work in the one-dimensional case of Christol, Dwork, Robba, Young, et al.
Our results do not require positive residue characteristic; thus besides their
relevance to the study of Swan conductors for isocrystals, they are germane to
the formal classification of flat meromorphic connections on complex manifolds.
