Abstract

It is known that a closed 2-sided stable minimal hypersurface in a 4-manifold with positive scalar curvature (PSC) must be Yamabe positive, and hence it is diffeomorphic to a connected sum of S¹ x S² ’s and spherical space forms.  We show that using a new compactness result for minimal surfaces in covering spaces and techniques from 4-manifold topology, one can obtain further control on the topology of stable minimal hypersurfaces.  As an application, we show that the outermost apparent horizons of a smooth, asymptotically flat manifold with nonnegative scalar curvature must be diffeomorphic to S³ or connected sums of S¹ x S² ’s.  This is an extension of Hawking’s black hole topology theorem to dimension 4.  The talk is based on joint work with Chao Li.

 

Link Information: https://us02web.zoom.us/j/81561992327?pwd=QCP07BLVk4TxnanLmZ0N8QjYammL8w.1

Meeting ID: 815 6199 2327

Passcode: 277350

 

Organizers: Nicolau Sarquis Aiex (NTNU), Siao-Hao Guo (NTU), Chung-Jun Tsai (NTU)