On maximal surfaces in Minkowski and asymptotically flat spacetimes

Come join us in this mini course given by Albachiara Cogo.

Abstract

Maximal surfaces are spacelike hypersurfaces of a Lorentzian manifold which locally maximize the area functional. They are very important tools in General Relativity since they somehow reflect some properties of the ambient spacetime; for example, foliations by maximal slices played a crucial role in the first proofs of the positive mass theorem and in the analysis of global stability of Minkowski.

In this mini course we will first go through the main ideas involved in the existence results of maximal surfaces in Minkowski and in asymptotically flat spacetimes, recalling the arguments provided by R. Bartnik. We will deal with both the variational formulation of the maximization of the area functional and the quasi-linear elliptic PDE which arises from its Euler-Lagrange equation and which geometrically describes the vanishing of the mean curvature.

In addition, referring to the results of Cheng—Yau and Ecker, we will discuss some crucial results regarding entire area maximizing hypersurfaces, in order to finally present some recent developments of my PhD project under the supervision of G. Huisken.

Location

The mini course will happen at Auditório do IME on 25, 26 and 29 of august, from 14h00 to 15h30, with simultaneous transmission through this link.