A Remark on Gauge Transformations and the Moving Frame Method

Details A Remark on Gauge Transformations and the Moving Frame Method A Remark on Gauge Transformations and the Moving Frame Method

2009-06-10

arxiv.org/abs/0906.1972v1

AnIHPC 27 (2010) 503-515

Mathematics

Analysis of PDEs

17 pages

Scientific paper

10.1016/j.anihpc.2009.09.004

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.

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