A remark on gauge transformations and the moving frame method
By Armin Schikorra. 2009
84 citations recorded by the source corpus.
Abstract In this note we give a shorter proof of recent regularity results on elliptic partial differential equations with antisymmetric structure presented in Riviere (2007) [23] , Riviere and Struwe (2008) [24] . We differ from the mentioned articles in using the direct method of Helein's moving frame, i.e. minimizing a certain variational energy-functional, in order to construct a suitable gauge transformation. Though this is neither new nor surprising, it enables us to describe a proof of regularity using elementary arguments of calculus of variations and algebraic identities. Moreover, we remark that in order to prove Hildebrandt's conjecture on regularity of critical points of 2D-conformally invariant variational problems one can avoid the application of the Nash–Moser imbedding theorem.
Subfields: Applied Mathematics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/229100f49f4ab77fd0bd5a9ebf66bd04c6a0e206
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In Applied Mathematics
In Statistical and Nonlinear Physics
Citations in the corpus
- Fractional div-curl quantities and applications to nonlocal geometric equations (2017, methodology): “By an adaptation of techniques due to Uhlenbeck [52], see also [33], he then constructed a gauge P ∈ Ẇ (1,2)(R(2), SO(N)), such that (1.”
- Regularity of n/2-harmonic maps into spheres (2010, methodology): “Uhlenbeck’s results in gauge theory [Uhl82] in order to implement div-curl expressions in the Euler-Lagrange equations, a technique which can be reinterpreted as an extension of Hélein’s moving frame method; see [Sch10a].”