  A slice distance for the class of weak abelian Lp-bundles in 3 dimensions was
introduced in a previous article in collaboration with Tristan Rivi\`ere, where
it was used to prove the closure of such class of bundles for the weak
Lp-convergence. We further investigate this distance here, and we prove more
properties of it, for example we show that it is H\"older-continuous on the
slices. Using the same distance, we give here a notion of a boundary trace,
giving a suitable setting for minimization problems on weak bundles. We then
state some conjectures and some open questions.
