Program of the BFZ Seminar on November 14, 2014

Jeremie Szeftel (CNRS/Paris): Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space

Abstract: We study time-like hypersurfaces with vanishing mean curvature in the 3+1 dimensional Minkowski space, which are the hyperbolic counterparts to the minimal surface equation. 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.

Ernst Kuwert (Freiburg i. Br.): Local solutions to a free boundary problem for the Willmore functional

Abstract: Given a smooth domain Ω in ℝ³, we construct Willmore disks which are critical in the class of surfaces meeting ∂Ω orthogonally along their boundary and having small prescribed area.

Pierangelo Marcati (GSSI and University of L'Aquila):


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