 Uhlenbeck small-energy Coulomb gauge

For a connection with compact structure group on a four-dimensional ball, sufficiently small $L^2$ curvature permits a gauge with $d^{\ast }a=0$, suitable boundary condition and $\Vert a{\Vert }_{W^{1,2}}\le C\Vert F{\Vert }_2$ after rescaling. For anti-self-dual connections, local elliptic regularity also gives scale-invariant curvature derivative estimates on smaller balls. These are local analytic inputs, not the global bubbling compactness conclusion.

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