浙大-西湖几何分析讨论班——Asymptotic stability of the Simons cone for the spherically symmetric timelike extremal hypersurfaces in Minkowski space

Abstract:

The Simons cone is known as a counter-example of Bernstein conjecture for the minimal surface equation. This celebrated minimal surface is a stationary solution of the timelike extremal hypersurface equation in higher dimension. In this talk, we introduce asymptotic stable of the Simons cone for the vanishing mean curvature flow in higher dimension. 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.