Memoirs of the American Mathematical Society 2013; 99 pp; softcover Volume: 223 ISBN10: 082184489X ISBN13: 9780821844892 List Price: US$69 Individual Members: US$41.40 Institutional Members: US$55.20 Order Code: MEMO/223/1047
 This monograph contains a study of the global Cauchy problem for the YangMills equations on \((6+1)\) and higher dimensional Minkowski space, when the initial data sets are small in the critical gauge covariant Sobolev space \(\dot{H}_A^{(n4)/{2}}\). Regularity is obtained through a certain "microlocal geometric renormalization" of the equations which is implemented via a family of approximate null Crönstrom gauge transformations. The argument is then reduced to controlling some degenerate elliptic equations in high index and nonisotropic \(L^p\) spaces, and also proving some bilinear estimates in specially constructed squarefunction spaces. Table of Contents  Introduction
 Some gaugetheoretic preliminaries
 Reduction to the "main apriori estimate"
 Some analytic preliminaries
 Proof of the main apriori estimate
 Reduction to approximate halfwave operators
 Construction of the halfwave operators
 Fixed time \(L^2\) estimates for the parametrix
 The dispersive estimate
 Decomposable function spaces and some applications
 Completion of the proof
 Bibliography
