A Spacetime Alexandrov Theorem
 Title:
 A Spacetime Alexandrov Theorem
 Author(s):
 Wang, YeKai
 Thesis Advisor(s):
 Wang, MuTao
 Date:
 2014
 Type:
 Dissertations
 Department(s):
 Mathematics
 Persistent URL:
 http://dx.doi.org/10.7916/D8MG7MN2
 Notes:
 Ph.D., Columbia University.
 Abstract:
 Let Σ be an embedded spacelike codimension2 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 codimension2 submanifolds using conformal KillingYano 2forms. The Minkowski formula is then combined with a HeintzeKarcher type geometric inequality to prove the main theorem. We also obtain several rigidity results for codimension2 submanifolds in spherically symmetric spacetimes.
 Subject(s):
 Mathematics
 Item views
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 Suggested Citation:
 YeKai Wang, 2014, A Spacetime Alexandrov Theorem, Columbia University Academic Commons, http://dx.doi.org/10.7916/D8MG7MN2.