4 problems

Let $\mathcal L\subset\mathbb{R}^n$ be an affine subspace satisfying Hypothesis D. Let $\mathcal M\subset\mathcal L$ be a smooth manifold which is non-degenerate when viewed as a m…

An affine subspace of Euclidean space is a set of the form … It is of Khintchine type for divergence when the divergence conclusion of Khintchine's theorem holds after restricting…

Let $\mathscr{H}$ be an affine subspace, represented by a matrix $\widetilde{A}$, and let $\omega_i(\widetilde{A})$, $1\le i\le n-d$, denote its higher-order Diophantine exponents.…

Let $d\geq 1$, let $0\leq k<d$, and let $\boldsymbol{x}\in\mathbb{R}^{d-k}$. An affine coordinate subspace $\{\boldsymbol{x}\}\times\mathbb{R}^k\subseteq\mathbb{R}^d$ is of Khintch…