Stable Yang–Mills connection

In differential geometry and especially Yang–Mills theory, a (weakly) stable Yang–Mills (YM) connection is a Yang–Mills connection around which the Yang–Mills action functional is positively or even strictly positively curved. Yang–Mills connections are solutions of the Yang–Mills equations following from them being local extrema of the curvature, hence critical points of the Yang–Mills action functional, which are determined by a vanishing first derivative of a variation. (Weakly) stable Yang–Mills connections furthermore have a positive or even strictly positive curved neighborhood and hence are determined by a positive or even strictly positive second derivative of a variation.

(Weakly) stable Yang–Mills connections are named after Yang Chen-Ning and Robert Mills.