This result states first variation formulae for minimal immersions and harmonic maps: given (N n,h) be a Riemannian manifold. For the area functional, let F:M m N be a smooth immersion, let M be a relatively compact open set, and let g F := F *h be the induced.... It is useful in harmonic map theory and elliptic regularity, where variational identities, curvature estimates, and compactness arguments control geometric objects.