Geometry and Topology Seminar - Pei-Ken Hung - Toroidal positive mass theorem
Title: Toroidal positive mass theorem
Abstract: We establish the positive mass theorem for 3-dimensional asymptotically hyperboloidal initial data sets with toroidal infinity. In the umbilic case, a rigidity statement is proven showing that the total mass vanishes precisely when the initial data manifold is isometric to a portion of the canonical slice of the associated Kottler spacetime. Furthermore, we provide a new proof of the recent rigidity theorems of Eichmair-Galloway-Mendes in dimension 3, with weakened hypotheses in certain cases. These results are obtained through an analysis of the level sets of spacetime harmonic functions. This is a joint work with Aghil Alaee and Marcus Khuri.
Location: Virtual, Zoom
ID: 637 674 6854Passcode: Topology