Bogomolov restriction theorem for Higgs bundles

Let (E,θ)(E,θ) be a stable Higgs bundle of rank r on a smooth complex projective surface X equipped with a polarization H  . Let C⊂XC⊂X be a smooth complete curve with [C]=n⋅H[C]=n⋅H. If2n>Rr(2rc2(E)−(r−1)c1(E)2), where R=max{(rs)(r−1s−1):1⩽s⩽r−1}, then we prove that the restriction of (E,θ)(E,θ) to C is a stable Higgs bundle. This is a Higgs bundle analog of Bogomolov's restriction theorem for stable vector bundles.