Stability and energy identity for Yang–Mills–Higgs pairs

In this paper, we study the properties of critical points Yang-Mills-Higgs functional, which are called pairs. We first consider weakly stable pairs on a vector bundle over S^n (n > 3). When n 3, prove that norm its Higgs field is 1 and connection actually Yang-Mills. More precisely, curvature vanishes when 4. also use bubble-neck decomposition to energy identity sequence 4-dimensional compact manifold with uniformly bounded energy. show there subsequence converges smoothly pair up gauge modulo finitely many spheres Yang-Mills connections.