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Title:
Energy Identity for Stationary Yang-Mills
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Abstract:
Given a sequence of stationary Yang-Mills A_i->A one often understands blow up through the defect measure of the sequence. The energy identity explicitly relates the energy density of the defect measure to the energy of bubbles appearing at this point. This identity has been known for instantons but has only been a conjectural picture for general stationary sequences. We will describe this picture in detail and then describe the techniques involved in the recent proof of this result on general stationary sequences. The techniques also allow us to prove a conjectured W^{2,1} estimate on the curvature, that is, for a stationary connection A the hessian of the curvature F_A has apriori estimates in L^1. The main new technical achievement is the introduction of a new notion of gauge, which we call harmonic \epsilon-gauges, as well a new log-superconvexity estimate for these gauges. The produced estimates are the main ones required in the proof of the results. This is joint work with Daniele Valtorta.
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