This result states energy density constancy for harmonic maps under nonnegative ricci and nonpositive sectional curvature: given (M,g) be a connected compact Riemannian manifold without boundary, let Ric M 0, and let (N,h) have K N 0. If u:M N is smooth and harmonic, and if the energy density e(u):M.... It is useful in harmonic map theory and elliptic regularity, where variational identities, curvature estimates, and compactness arguments control geometric objects.