This result states allard regularity theorem, simplified corollary form: In the simplified form used in this course, let V be an integral m-varifold in B(x 0,r) R n with generalized mean curvature H L p(\|V\|) for some p > m, and suppose x 0 spt V. For.... It is useful in geometric measure theory and minimal surface regularity, where variational identities, curvature estimates, and compactness arguments control geometric objects.