Let $p,q \geq 1$ be integers, and define the cone

\begin{align*} C_{p,q} = \{(x,y)\in \mathbb{R}^{p+1}\times\mathbb{R}^{q+1}: q|x|^2=p|y|^2\}. \end{align*}

Then the regular hypersurface $C_{p,q}^{\mathrm{reg}}:=C_{p,q}\setminus\{0\}$ is minimal in $\mathbb{R}^{p+q+2}$. In the symmetric case $p=q=3$, the Simons cone $C_{3,3}\subset \mathbb{R}^8$ is stable away from the vertex: for every compactly supported smooth normal variation field $V=\phi\nu$ on $C_{3,3}^{\mathrm{reg}}$, where $\nu:C_{3,3}^{\mathrm{reg}}\to \mathbb{S}^7$ is a smooth unit normal field and $\phi\in C_c^\infty(C_{3,3}^{\mathrm{reg}})$, the second variation of $7$-dimensional area satisfies

\begin{align*} \delta^2 A_{C_{3,3}}[\phi\nu]\geq 0. \end{align*}