The Yang-Mills fields on curved space-times

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Written by Sari Ghanem

I will present the proof of the non-blow up of the Yang-Mills curvature on arbitrary curved space-times using a Kirchoff-Sobolev type representation formula derived by Klainerman and Rodnianski, combined with suitable Grönwall type inequalities. While the argument of Chruściel and Shatah requires a control on two derivatives of the Yang-Mills curvature, we can get away by controlling only one derivative instead, and write a new gauge independent proof of the non-blow up of the Yang-Mills curvature on arbitrary, fixed, sufficiently smooth, globally hyperbolic, curved 4-dimensional Lorentzian manifolds.