This result states schoen curvature estimate for stable minimal surfaces: given (M 3,g) be a smooth Riemannian three-manifold, let p M, and let r 0 > 0. Suppose that the geodesic ball B M(p,r 0) satisfies |sec M| for some 0, and that inj M(x) i 0 for.... It is useful in minimal surfaces and harmonic maps, where variational identities, curvature estimates, and compactness arguments control geometric objects.