Event № 370
The global structure of solutions to the Einstein equations can be analyzed by studying the evolution of geometric quantities under the Einstein flow. An approach to the general problem of understanding the global geometry of space time is the non-linear stability problem, which considers initial data close to explicitly known solutions and analyzes their future development. The stability question is essential in Mathematical Relativity and is only understood for a few explicit solutions. In this talk we present results on the stability of solutions to the Einstein equations in 2+1 dimensions in the presence of Vlasov matter without symmetry assumptions. We discuss a technique of constructing geometric energies for distribution functions of this type of matter and how these are used to provestability. In addition, we construct future complete and stable solutions to the Einstein flow on the 2-sphere - a result which is shown to be an exclusive feature of Vlasov matter in 2+1 dimensions.