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.