On 3+1 Lorentzian Einstein manifolds with one rotational isometry

Abstract:  Differentiable manifolds whose Ricci curvature is proportional to the metric are called Einstein manifolds. Such manifolds have been central objects of study in differential geometry and Einstein's theory for general relativity, with some strong recent results. In this talk, we shall focus on positively curved 3+1 Lorentzian Einstein manifolds with one spacelike rotational isometry. After performing the dimensional reduction to a 2+1 dimensional Einstein's equations coupled to 'shifted' wave maps, we shall prove two explicit positive mass theorems:  

i)           for CMC slices in expanding region

ii)          for maximal slices in 'stationary' region.