The volume of marginally trapped submanifolds in a Lorentzian manifold satisfying the null energy condition
Abstract
In this paper, we focus on a marginally trapped submanifold $f:\Sigma^n \to M^{n+2}_1$ in a Lorentzian manifold $M^{n+2}_1$. We show that $f$ lies in a certain null hypersurface $\mathcal{N}_f^{n+1}$ in $M^{n+2}_1$ and $f$ has a locally volume-maximizing property in $\mathcal{N}_f^{n+1}$ if $M^{n+2}_1$ satisfies the null energy condition.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Geometry and complex manifolds
Publication details
- Journal / source
- Kodai Mathematical Journal
- Publisher
- Tokyo Institute of Technology, Department of Mathematics
- Volume
- 49
- Issue
- 2
- Pages
- 193-203
- Publication date
- 30 June 2026
- Language
- EN