Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
The timelike minimal surface equation is a degenerate hyperbolic system describing the motion of a relativistic membrane, or p-brane. Using a harmonic map gauge, Olaf Milbredt has obtained local well-posedness results for the corresponding Cauchy-Problem under suitable geometric assumptions. Much less is known, however, about global well-posedness and stability of a solution with respect to small-data perturbations when the spacetime is not Minkowski-Space. In this talk I shall give an introduction to the theory aswell as a short overview of the existing literature and then present some stability results for the case of a membrane moving in an expanding spacetime that is not necessarily spatially homogenuous.