  We examine the evolution of an Ising ferromagnet endowed with
zero-temperature single spin-flip dynamics. A large droplet of one phase in the
sea of the opposite phase eventually disappears. An interesting behavior occurs
in the intermediate regime when the droplet is still very large compared to the
lattice spacing, but already very small compared to the initial size. In this
regime the shape of the droplet is essentially deterministic (fluctuations are
negligible in comparison with characteristic size). In two dimensions the shape
is also universal, that is, independent on the initial shape. We analytically
determine the limiting shape of the Ising droplet on the square lattice. When
the initial state is a semi-infinite stripe of one phase in the sea of the
opposite phase, it evolves into a finger which translates along its axis. We
determine the limiting shape and the velocity of the Ising finger on the square
lattice. An analog of the Ising finger on the cubic lattice is the translating
Ising soliton. We show that far away from the tip, the cross-section of the
Ising soliton coincides with the limiting shape of the two-dimensional Ising
droplet and we determine a relation between the cross-section area, the
distance from the tip, and the velocity of the soliton.
