  We prove that, for a $p$-divisible group with additional structures over a
complete valuation ring of rank one $O_K$ with mixed characteristic $(0,p)$, if
the Newton polygon and the Hodge polygon of its special fiber possess a non
trivial contact point, which is a break point for the Newton polygon, then it
admits a "Hodge-Newton filtration" over $O_K$. The proof is based on the
theories of Harder-Narasimhan filtration of finite flat group schemes and
admissible filtered isocrystals. We then apply this result to the study of some
larger class of Rapoport-Zink spaces and Shimura varieties than those studied
previously by Mantovan, and confirm some new cases of Harris's conjecture.

Number Theory