Homogenization and 3D-2D dimension reduction of a functional on manifold valued Sobolev spaces

We study simultaneous homogenization and dimensional reduction of integral functionals for maps in manifold-valued Sobolev spaces. Due to the superlinear growth regime, we prove that the density of the $\mathrm{\Gamma }$-limit is a tangential quasiconvex integrand represented by a cell formula.