On badly approximable subspaces

Given an $a$-dimensional linear subspace $\mathfrak{A}$ in ${\mathbb{R}}^d$ which contains a badly approximable $b$-dimensional subspace $\mathfrak{B} \subset \mathfrak{A}$\mathrm{.}Westudythebadlyapproximabilityalmostall$c$-dimensionallinearsubspaces$\mathfrak{C} \subset \mathfrak{A}$.