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Stability of de Sitter space under Lorentzian constant mean curvature flow

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If you have a question about this talk, please contact Harsha Hutridurga .

Time-like constant mean curvature hypersurfaces in Minkowski space are one way to model extended test bodies evolving under a constant normal force. The associated equations are quasilinear hyperbolic partial differential equations, for which we study the Cauchy problem. An explicit solution is an appropriately-rescaled de Sitter space, with the usual hyperboloidal embedding. We discuss the nonlinear stability of this solution, focussing on the geometric obstructions, and their resolutions, that arise when passing from the homogeneous case to the inhomogeneous case.

This talk is part of the Geometric Analysis & Partial Differential Equations seminar series.

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