On stability of the catenoid under vanishing mean curvature flow on Minkowski space

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\partial_t^2 u(t,x)-\partial_x^2 u(t,x)+V(x)u(t,x)=0.

The potential

V

is assumed to be smooth with asymptotic behavior

V(x)\sim -\tfrac14 |x|^{-2}\mbox{ as } |x|\to \infty.

...

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We study time-like hypersurfaces with vanishing mean curvature in the (3+1) dimensional Minkowski space, which are the hyperbolic counterparts to minimal embeddings of Riemannian manifolds. The catenoid is a stationary solution of the associated Cauchy pro ...

On stability of the catenoid under vanishing mean curvature flow on Minkowski space

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Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space