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We study the geometry of unitary Shimura varieties without assuming theexistence of an ordinary locus. We prove, by a simple argument, the existenceof canonical subgroups on a strict neighborhood of the $\mu$-ordinary locus(with an explicit bound). We then define the overconvergent modular forms (ofclassical weight), as well as the relevant Hecke operators. Finally, we showhow an analytic continuation argument can be adapted to this case to prove aclassicality theorem, namely that an overconvergent modular form which is aneigenform for the Hecke operators is classical under certain assumptions.

Analytic continuation on Shimura varieties with $\mu$-ordinary locus