  The entropy of a hypersurface is given by the supremum over all F-functionals
with varying centers and scales, and is invariant under rigid motions and
dilations. As a consequence of Huisken's monotonicity formula, entropy is
non-increasing under mean curvature flow. We show here that a compact mean
convex hypersurface with some low entropy is diffeomorphic to a round sphere.
We will also prove that a smooth self-shrinker with low entropy is exact a
hyperplane.
