Title: Corona limits of tilings : Periodic case,
Abstract: We study the limit shape of successive coronas of a tiling, which models the
growth of crystals. We define basic terminologies and discuss the existence and
uniqueness of corona limits, and then prove that corona limits are completely
characterized by directional speeds. As an application, we give another proof
that the corona limit of a periodic tiling is a centrally symmetric convex
polyhedron (see [Zhuravlev 2001], [Maleev-Shutov 2011]).