Analogously in the context of HYM connections, if a holomorphic bundle $E$ is unstable, then its Harder-Narasimhan decomposition provides a lower bound on the Yang-Mills energy of any Chern connection on $E$ compatible with $\bar{\partial}_{E}$, which improves the topological energy bound. This type of phenomenon is common in Kähler geometry, for instance it also happens in the context of K-stability. These topics are covered in the introduction of [30].