Stability of timelike minimal surfaces in expanding spacetimes

30.11. bis 30.11.2021, 12:15-13:45  –  Room Campus Golm, C9A03 Tübingen
Geometric Analysis, Differential Geometry and Relativity

Philip Thonke

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.

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