  We show by a formal asymptotic expansion that level sets of solutions of a
time-fractional Allen-Cahn equation evolve by a geometric flow whose normal
velocity is a positive power of the mean curvature.
  This connection is quite intriguing, since the original equation is nonlocal
and the evolution of its solutions depends on all previous states, but the
associated geometric flow is of purely local type, with no memory effect
involved.
