Felix Finster: Geometry and analysis of asymptotically flat manifolds of small mass

Anstract: After a brief introduction to mathematical relativity, we review the positive mass theorem 
for asymtotically flat manifolds and the Riemannian Penrose inequalities. 
The geometry of asymptotically flat manifolds of small mass is discussed. 
By analyzing the level sets of the Witten spinor, we derive inequalities which quantify 
that the curvature of such manifolds is small except on sets of small surface area.