  In this note we give a shorter proof of recent regularity results by Riviere
and Riviere-Struwe. We differ from the mentioned articles only in using the
direct method of Helein's moving frame to construct a suitable gauge
transformation. Though this is neither new nor surprising, it enables us to
describe a proof of regularity using besides the duality of Hardy- and
BMO-space only elementary arguments of calculus of variations and algebraic
identities. Moreover, we remark that in order to prove Hildebrandt's conjecture
one can avoid the Nash-Moser imbedding theorem. There are no new results
presented here, nor are there any techniques we could claim originality for.
