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.
