English

A Remark on Gauge Transformations and the Moving Frame Method

Analysis of PDEs 2013-01-23 v1

Abstract

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.

Cite

@article{arxiv.0906.1972,
  title  = {A Remark on Gauge Transformations and the Moving Frame Method},
  author = {Armin Schikorra},
  journal= {arXiv preprint arXiv:0906.1972},
  year   = {2013}
}

Comments

17 pages

R2 v1 2026-06-21T13:12:03.871Z