A Spacetime Alexandrov Theorem
Let Σ be an embedded spacelike codimension-2 submanifold in a spherically symmetric spacetime satisfying null convergence condition. Suppose Σ has constant null mean curvature and zero torsion. We prove that Σ must lie in a standard null cone. This generalizes the classical Alexandrov theorem which classifies embedded constant mean curvature hypersurfaces in Euclidean space. The proof follows the idea of Ros and Brendle. We first derive a spacetime Minkowski formula for spacelike codimension-2 submanifolds using conformal Killing-Yano 2-forms. The Minkowski formula is then combined with a Heintze-Karcher type geometric inequality to prove the main theorem. We also obtain several rigidity results for codimension-2 submanifolds in spherically symmetric spacetimes.
Academic Commons
Wang, Ye-Kai
Author
Wang, Mu-Tao
Thesis advisor
Columbia University. Mathematics
Originator
Theses
English
Mathematics
text
2014
eng
2017-06-08T20:22:55Z
2017-11-10T03:13:34Z
Ph.D.
2
Mathematics
Columbia University
10.7916/D8MG7MN2