  An Abelian differential gives rise to a flat structure (translation surface)
on the underlying Riemann surface. In some directions the directional flow on
the flat surface may contain a periodic region that is made up of maximal
cylinders filled by parallel geodesics of the same length. The growth rate of
the number of such regions counted with weights, as a function of the length,
is quadratic with a coefficient, called Siegel-Veech constant, that is shared
by almost all translation surfaces in the ambient stratum. We evaluate various
Siegel-Veech constants associated to the geometry of configurations of periodic
cylinders and their area, and study extremal properties of such configurations
in a fixed stratum and in all strata of a fixed genus.
