In differential geometry, Huisken's monotonicity formula states that, if an n-dimensional surface in (n + 1)-dimensional Euclidean space undergoes the mean curvature flow, then its convolution with an appropriately scaled and time-reversed heat kernel is non-increasing. The result is named after Gerhard Huisken, who published it in 1990. Specifically, the (n + 1)-dimensional time-reversed heat kernel converging to a point x0 at time t0 may be given by the formula Then Huisken's monotonicity formula gives an explicit expression for the derivativeof