Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space (BOK)
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This monograph contains a study of the global Cauchy problem for the Yang-Mills equations on (6+1) and higher dimensional Minkowski space, when the initial data sets are small in the critical gauge covariant Sobolev space H?(n?4)/2A. Regularity is obtained through a certain "microlocal geometric renormalization" of the equations which is implemented via a family of approximate null Cronstrom gauge transformations. The argument is then reduced to controlling some degenerate elliptic equations in high index and non-isotropic Lp spaces, and also proving some bilinear estimates in specially constructed square-function spaces.