  We propose that domain walls formed in a classical Ginzburg-Landau model can
exhibit topologically stable but thermodynamically metastable states. This
proposal relies on Allen-Cahn's assertion that the velocity of domain wall is
proportional to the mean curvature at each point. From this assertion we
speculate that domain wall behaves like a rubber band that can winds the
background geometry in a nontrivial way and can exist permanently. We
numerically verify our proposal in two and three spatial dimensions by using
various boundary conditions. It is found that there are possibilities to form
topologically stable domain walls in the final equilibrium states. However,
these states have higher free energies, thus are thermodynamically metastable.
These metastable states that are protected by topology could potentially serve
as storage media in the computer and information technology industry.
