  We consider the flat flow approach for the mean curvature equation with
forcing in an Euclidean space $\mathbb R^n$ of dimension at least 2. Our main
results states that tangential balls in $\mathbb R^n$ under any flat flow with
a bounded forcing term will experience fattening, which generalizes the result
by Fusco, Julin and Morini from the planar case to higher dimensions. Then, as
in the planar case, we are able to characterize stationary sets in $\mathbb
R^n$ for a constant forcing term as finite unions of equisized balls with
mutually positive distance.
