Geometric and Asymptotic Properties of Brillouin Zones in Lattices

Each lattice in R^d determines a sequence of Brillouin zonesB_n, fundamental regions for bounded by Bragg hyperplanes; forexample B₁ is the Dirichlet region. Basic geometric and topologicalproperties of these zones are established, and we obtain asymptoticestimates (valid for almost all ) for (n) = , where L(n) is the number of connected componentsof the interior of B_n (called Landsberg subzones). Fermi surfacesare also briefly described.