This result states almgren–federer dimension bound for area-minimizing currents: given U R n be open, and let T be an area-minimizing integral m-current in U with T = 0 in U. Then the interior singular set satisfies H (sing T) m-2. If n=m+1, so that T is a.... It is useful in geometric measure theory and minimal surface regularity, where variational identities, curvature estimates, and compactness arguments control geometric objects.