Inserted: 5 feb 2012
Last Updated: 5 feb 2012
A slice distance for the class of weak abelian $L^p$-bundles in $3$ dimensions was introduced in previous work with Tristan Rivière, where it was used to prove the closure of such class of bundles for the weak $L^p$-convergence. We further investigate this distance here, and we prove more properties of it, for example we show that it is Hölder-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.
Keywords: Slice distance, trace definition, vectorfields with integer fluxes, topological