%0 Journal Article %T A note of semistable Higgs bundles over compact K£¿hler manifolds %A Yanci Nie %A Xi Zhang %J Mathematics %D 2015 %I arXiv %X In this note, by using the Yang-Mills-Higgs flow, we show that semistable Higgs bundles with vanishing the first and second Chern numbers over compact K\"aher manifolds must admit a filtration whose quotients are Hermitian flat Higgs bundles. %U http://arxiv.org/abs/1506.02146v1