A central leaf C(x) passing through a point x in the Siegel modular variety A_g (modulo p) of genus g is the locus which consists of the points whose associated polarized p-divisible groups are isomorphic to that of x. We are interested in how the size of C(x) changes when x varies in the moduli space. In particular how large can C(x) be (if finite) and when C(x) is a singleton (the Gauss problem). In this talk we shall discuss these questions and explain our result on the Gauss problem. This is joint work with Tomoyoshi Ibukiyama and Valentijn Karemaker.