A monotonicity formula for mean curvature flow with surgery

We prove a monotonicity formula for mean curvature flow with surgery. This formula differs from Huisken's monotonicity formula by an extra term involving the mean curvature. As a consequence, we show that a surgically modified flow which is sufficiently close to a smooth flow in the sense of geometric measure theory is, in fact, free of surgeries. This result is used in the analysis of mean curvature flow with surgery in Riemannian three-manifolds (cf. [5]).