  An anisotropic surface energy is the integral of an energy density that
depends on the normal at each point over the considered surface, and it is a
generalization of surface area. The minimizer of such an energy among all
closed surfaces enclosing the same volume is unique and it is (up to rescaling)
so-called the Wulff shape. We prove that, unlike the isotropic case, there
exists an anisotropic energy density function such that there exist closed
embedded equilibrium surfaces with genus zero in the three-dimensional
Euclidean space each of which is not (any homothety and translation of) the
Wulff shape. We also give nontrivial self-similar shrinking solutions of
anisotropic mean curvature flow. These results are generalized to hypersurfaces
in the (n+1)-dimensional Euclidean space.
