This result states eells-sampson subharmonicity inequality: given u:(M,g) (N,h) be a smooth harmonic map. Assume Ric M 0 and K N 0. Then g e(u) | du| 2 0. In particular, e(u) is subharmonic.. It is useful in harmonic map theory and elliptic regularity, where variational identities, curvature estimates, and compactness arguments control geometric objects.