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

Monday, October 28, 2013 -
3:15pm to 4:15pm
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 problem. This solution is linearly unstable, and we show that this instability is the only obstruction to the global nonlinear stability of the catenoid. More precisely, we prove in a certain class of symmetry the existence, in the neighborhood of the catenoid initial data, of a co-dimension 1 Lipschitz manifold transverse to the unstable mode consisting of initial data whose solutions exist globally in time and converge asymptotically to the catenoid. This is joint work with Roland Donninger, Joachim Krieger and Willie Wong.
Jeremie Szeftel
Université Pierre et Marie Curie
Event Location: 
Fine Hall 314