The resolution of the Yang-Mills Plateau problem in super-critical dimensions

We then prove the optimal regularity result for solutions of this Plateau problem. On the way to prove this result we establish a Coulomb gauge extraction theorem for weak curvatures with small Yang-Mills density. This generalizes to the general framework of weak L2 curvatures previous works of Meyer-Rivière and Tao-Tian in which respectively a strong approximability property and an admissibility property were assumed in addition.