Let $(X^2,g)$ be a hyperkahler ALE orbifold surface. Consider its Ricci deformation equation: $$ \Delta h+2Rm(h)=0 $$ for $\text{div}_g h=\text{Tr}_gh=0$ and $h=O(r^{-\epsilon})$ as $r \to +\infty$. Moreover, we require that $h$ is smooth at any orbifold point of $X$.
Given any such $h$, can we conclude that $h=0$ at any orbifold point?
