Timeline for Uhlenbeck's theorem novelty
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 20, 2021 at 17:39 | comment | added | Liviu Nicolaescu | I think that in her paper on the removal of singularities you see this phenomenon better. Technically the bound on energy is required by the method. The Coulomb gauge is found by solving a nonlinear equation using the implicit function theorem. | |
| Apr 19, 2021 at 17:23 | comment | added | Leo Moos | Do you know a reference expanding on the last paragraph? I'd be especially curious to find out more about situations where a Coulomb gauge exists despite the curvature being 'large', that is $\lvert F \rvert_{L^2(D)} > \epsilon$ or $4 \pi^2$ say. | |
| Apr 19, 2021 at 17:11 | history | edited | Liviu Nicolaescu | CC BY-SA 4.0 |
added 142 characters in body
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| Dec 13, 2014 at 15:02 | vote | accept | Jjm | ||
| Dec 10, 2014 at 9:53 | comment | added | Igor Khavkine | @DeaneYang, I'm well aware, thanks. I could also rephrase my comment by saying that Uhlenbeck's "Coulomb gauge", when the "imaginary time" is replaced by "real time", becomes the Lorenz gauge, rather than the usual Coulomb gauge in electrodynamics or Yang-Mills theory. But I imagine the incongruence isn't going to go away since all of this terminology already seems to have become standard. | |
| Dec 10, 2014 at 4:07 | comment | added | Deane Yang | Igor, this is in 4 dimensions, but time $t$ has been replaced by "imaginary time" so that the metric is no longer Lorentzian but is Riemannian. | |
| Dec 9, 2014 at 23:18 | comment | added | Igor Khavkine | To a physicist, it is strange that this gauge fixing condition is referred to as "Coulomb gauge". It is true that in 4d electrodynamics this name refers to the condition that the divergence of the vector potential $\mathbf{A}_t$ is zero. However, here $\mathbf{A}_t$ should be interpreted as the pullback to the level sets of a special coordinate $t$ of a 1-form $A$ on $M$, with the divergence taken with respect to the induced metric on each level set. The simple divergence of $A$ on $M$ is called the Lorenz gauge and seems to be the more appropriate analog. | |
| Dec 9, 2014 at 22:07 | history | answered | Liviu Nicolaescu | CC BY-SA 3.0 |