On isoperimetric surfaces in Riemannian manifolds

Jan Metzger (Potsdam)

In this talk I will present joint work with Michael Eichmair. 

We consider the isoperimetric problem in asymptotically flat manifolds 
of arbitrary dimension which are close in $C^0$ to Schwarzschild. 
We show that for given large enough volume there exists a smooth connected 
isoperimetric surface enclosing this volume. 
If the metric is $C^2$-close to Schwazschild, the isoperimetric regions 
for large volume are unique. 
Furthermore, if the manifold has a relativistic center of mass, 
it is the asymptotic center of the boundaries of these regions.