The Simons cone is known as a counter-example of Bernstein conjecture for the minimal surface equation \( \textrm{div}\left( \frac{\nabla u}{\sqrt{1+|\nabla u|^2}}\right) =0, \quad \forall x\in \mathbb {R}^{d},\quad d\ge 8. \) This celebrated minimal surface is a stationary solution of the timelike extremal hypersurface equation \( \partial _t\left( \frac{\partial _t u}{\sqrt{1-|\partial _t u|^2+|\nabla u|^2}}\right) -\textrm{div}\left( \frac{\nabla u}{\sqrt{1-|\partial _t u|^2+|\nabla u|^2}}\right) =0 \) in higher dimension \(d\ge 8\) . We consider asymptotic stability of the Simons cone for the vanishing mean curvature flow in higher dimension \(d\ge 8\) . We prove that if the Simons cone is perturbed by a small radial symmetric initial data, then there exists a global unique solution of the vanishing mean curvature flow asymptotic to the Simons cone. It means that a unique global timelike extremal surface asymptotically to the Simons cone is constructed.
