Existence of approximate Hermitian-Einstein structures on semistable   principal bundles
  Let E_G be a principal G-bundle over a compact connected K\"ahler manifold, where G is a connected reductive complex linear algebraic group. We show that E_G is semistable if and only if it admits approximate Hermitian-Einstein structures. 
Indranil Biswas, Adam Jacob, Matthias Stemmler
math.DG math.AG