Nonexistence of stable discrete maps into some homogeneous spaces of nonnegative curvature

We consider stabilities for the weighted length or energy functional of a discrete map from a finite weighted graph $(X,m_E)$ into a smooth Riemannian manifold $(M,g)$. We prove the non-existence of a stable discrete minimal immersion or a non-constant stable discrete harmonic map from a finite weighted graph into certain homogeneous spaces, such as Kähler $C$-spaces of positive holomorphic sectional curvature and some simply-connected compact Riemannian symmetric spaces.