Oberseminar Mathematik in den Naturwissenschaften Jesse Ratzkin, Foliations of an asymptotically flat end by critical capacitors

Asymptotically flat manifolds provide models of a spacelike slice of spactime in the theory of general relativity. For this reason, it can be useful and interesting to construct canonical structures associated to an asymptotically flat end. We show that under appropriate conditions one can foliate an asymptotically flat end by hypersurfaces minimizing capacity, building on other constructions of foliations of asymptotically flat ends by special hypersurfaces. Along the way we discuss invertibility of the Dirichlet-to-Neumann map.

This is joint work with Moustapha Fall and Ignace Minlend.