We introduce an intrinsic notion of perimeter for subsets of
a general Minkowski space (i.e. a finite dimensional Banach space in which the
norm is not required to be even).
We prove that this notion of perimeter is equivalent to
the usual definition of surface energy for crystals and
we study the regularity properties of
the minimizers and the quasi-minimizers of perimeter.
In the two-dimensional case we obtain optimal regularity results:
apart from a singular set (which is ${\mathcal H}^1$-negligible and is empty when
the unit ball is neither
a triangle nor a quadrilateral), we find that quasi-minimizers can be locally
parameterized by means of a bi-lipschitz curve, while sets
with prescribed bounded curvature are, locally, lipschitz graphs.