Interpolation spaces and energy quantization for Yang–Mills fields

Tristan Rivière
2002 Communications in analysis and geometry  
In [19] G. Tian proved that the defect measure of a weakly converging sequence of Yang-Mills Fields on a riemannian manifold (M, g) of dimension n (n > 4) is carried by a n -4-rectifiable subset S of M. In the present paper we complete the picture of weakly converging sequences of YM Fields by proving that, in 4 dimension, the defect measure is quantized: at any point of S it is the sum of L 2 energies of YM fields on S' 4 . This result is extended to any dimension under some additional
more » ... additional assumption on the W 2 ' 1 norm of the curvature. In the last part we study non-linearities issued from curvatures in general and we prove that strong convergence in W 1)n l 2 of Coulomb gauges of connections over a n-dimensional manifold preserves the topology of the bundle at the limit.
doi:10.4310/cag.2002.v10.n4.a2 fatcat:bispa7ovjfez3c55rnv5iji7em