Approximate Hermitian-Yang-Mills structures on semistable principal   Higgs bundles
  We generalize the Hitchin-Kobayashi correspondence between semistability and the existence of approximate Hermitian-Yang-Mills structures to the case of principal Higgs bundles. We prove that a principal Higgs bundle on a compact Kaehler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure. 
Ugo Bruzzo and Beatriz Gra\~na Otero
math.CV math.AG math.DG