In 1985, Simon Donaldson showed that if is a nonsingular projective variety of complex dimension two, then a holomorphic vector bundle over admits a hermitian Yang-Mills connection if and only if the bundle is stable. A result of Yau and Karen Uhlenbeck generalized Donaldson's result to allow to be a compact Kähler manifold of any dimension. The Uhlenbeck-Yau method relied upon elliptic partial differential equations while Donaldson's used parabolic partial differential equations, roughly in parallel to Eells and Sampson's epochal work on harmonic maps.