... completedin the second paper. The third and fourth papers of this series will deal withhow the multi-valued graphs fit together and, in particular, prove regularity of the set of points of large ... GRAPHICAL OFF THE AXIS35In this part, we prove Theorem I.0.8 when the surface is in a slab, illus-trating the key points (the full theorem, using the results of this part, will beproved ... an improved gradient estimate, and consequently animproved bound for the growth of the separation between the sheets, for multi-valued minimal graphs:Proposition II.2.12. Given α>0, there...