Local Foliations of Constant Spacetime Mean Curvature Surfaces

19.10. bis 19.10.2021, 12:15-13:45  –  Room 2.09.2.22 Campus Golm, C9A03 Tübingen
Geometric Analysis, Differential Geometry and Relativity

Alejandro Penuela Diaz

Inspired by the small sphere limit for quasi-local masses we study local foliations of constant spacetime mean curvature surfaces, i.e. surfaces characterizing the center of mass in general relativity   and local foliations of constant expansion surfaces. Folowing the strategy used by Ye  to study local constant mean curvature foliations  we use a Lyapunov Schmidt reduction  in an N-dimensional manifold equipped with a symmetric 2-tensor to construct the foliations around a point, prove their uniqueness and show their nonexistence conditions.