On specializations of minimal $p$-divisible groups

In this paper, for any pair $(\zeta ,\xi )$ of Newton polygons with $\zeta \prec \xi$,weconstructaconcretespecializationfromtheminimal$p$-divisiblegroupof$\xi$totheminimal$p$-divisiblegroupof$\zeta$ by a beautiful induction. This in particular gives the affirmative answer to the unpolarized analogue of a question by Oort on the boundaries of central streams, and gives another proof of the dimension formula of the central leaves in the unpolarized case.