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 the leaf of the Hardt–Simon foliation with $\operatorname{dist}(T,0) = 1$. 

For all $R > 1$, the support of $T$ intersects $\partial B_R$ transversely. Thus $\operatorname{spt} \lVert T \rVert \cap \partial B_R$ is a smoothly embedded submanifold of $\partial B_R$; rescale this homothetically to $\Sigma_R \subset \partial B_1$.

 - For $R$ close enough one 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.** It would seem that this allows the absurd conclusion that the family of surfaces $(\Sigma_R)$ with $R \in [1+\frac{1}{N},N]$ say, gives an isotopy from $\mathbf{S}^{2n-2}$ to $\mathbf{S}^{n-1} \times \mathbf{S}^{n-1}$. What am I missing here?