  In this paper, we prove that in any compact Riemannian manifold with smooth
boundary, of dimension at least 3 and at most 7, there exist infinitely many
almost properly embedded free boundary minimal hypersurfaces. This settles the
free boundary version of Yau's conjecture. The proof uses adaptions of A.
Song's work and the early works by Marques-Neves in their resolution to Yau's
conjecture, together with Li-Zhou's regularity theorem for free boundary
min-max minimal hypersurfaces.
