Let $\mathbf{C}_S \subset \mathbf{R}^{2n}$ be a Simons cone, where the dimension is large enough that it is area-minimizing: $n \geq 4$. Let $T$ be a leaf of the Hardt–Simon foliation with $\operatorname{dist}(T,0) = 1$. For all $R > 1$, $T$ intersects $\partial B_R$ transversely. Thus $T \cap \partial B_R$ is a smoothly embedded submanifold of $\partial B_R$; rescale this homothetically to $\Sigma_R \subset \partial B_1$. - When $R$ is close to $1$, $\Sigma_R$ is diffeomorphic to the boundary of an $2n-1$-dimensional disk, so $\Sigma_R \simeq \mathbf{S}^{2n-2}$. - As $R \to \infty$, $\frac{1}{R} T \to \mathbf{C}_S$, so when $R$ is large enough then $\Sigma_R \simeq \mathbf{S}^{n-1} \times \mathbf{S}^{n-1}$. **Question.** The paradox is that the family $(\Sigma_R)$ gives an isotopy from $\mathbf{S}^{2n-2}$ to $\mathbf{S}^{n-1} \times \mathbf{S}^{n-1}$, where we let $R$ vary across $[1+\frac{1}{N},N]$ for example. What am I missing here?