Convergence conjecture for non-degenerate manifolds in affine subspaces

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 manifold in $\mathbb{R}^{\dim \mathcal L}\simeq\mathcal L$. The induced Lebesgue measure on $\mathcal M$ is called convergent Gallagher when the associated multiplicative Diophantine approximation set has measure zero whenever the relevant approximating series converges. Convergence conjecture for affine-subspace manifolds. The induced Lebesgue measure on $\mathcal M$ is convergent Gallagher. This statement extends the paper's convergence results for non-degenerate manifolds and for affine subspaces satisfying Hypothesis D to manifolds contained in such affine subspaces. The surrounding text presents it among open problems, so its resolution is not supplied here.