Stationary sets of the mean curvature flow with a forcing term

Abstract

We consider the flat flow approach for the mean curvature equation with forcing in R n . Our main results states that tangential balls in R n under any flat flow with a bounded forcing term will experience fattening, which generalizes the result in [9] from the planar case to higher dimensions. Then, as in the planar case, we are able to characterize stationary sets in R n for a constant forcing term as finite unions of equisize balls with mutually positive distance.