On the approximation of null hypersurfaces via maximal surfaces

09.02.2023, 14:15-15:45  –  2.22 und Zoom
Geometric Analysis, Differential Geometry and Relativity

Albachiara Cogo

Maximal surfaces are spacelike hypersurfaces of a Lorentzian manifold which are critical points of the area functional. They are very important tools in General Relativity and can be studied by applying non-linear PDEs techniques since the Euler-Lagrange equation of the variational problem of maximization of the area is a quasi-linear elliptic PDE that geometrically describes the vanishing of the mean curvature. Given the behavior of some simple solutions in Minkowski spacetime, it seems natural to investigate when sequences of maximal surfaces on exterior domains converge to null hypersurfaces. We will present some developments in this direction, referring to my ongoing Ph.D. project.

This talk is part of the seminar Geometric Analysis, Differential Geometry and Relativity organized by Carla Cederbaum (Uni Tübingen), Melanie Graf (Uni Tübingen), and Jan Metzger (Uni Potsdam) . To obtain the Zoom data please contact jan.metzger@uni-potsdam.de .