Stability and rigidity of extremal surfaces in Riemannian geometry and General Relativity

Abstract

We examine some common features of minimal surfaces, nonzero constant mean curvature surfaces and marginally outer trapped surfaces, concerning their stability and rigidity, and consider some applications to Riemannian geometry and general relativity.

arXiv comment21 pages. To appear in the book "Surveys in Geometric Analysis and Relativity celebrating Richard Schoen's 60th birthday."

References in corpus (6)

• A rotating black ring in five dimensions
• Isolated and dynamical horizons and their applications
• Local existence of dynamical and trapping horizons
• Rigidity and Positivity of Mass for Asymptotically Hyperbolic Manifolds
• Rigidity of area-minimizing two-spheres in three-manifolds
• Area-minimizing projective planes in three-manifolds

Cited by in corpus (4)

• On the Positive Mass, Penrose, an ZAS Inequalities in General Dimension
• On the geodesic incompleteness of spacetimes containing marginally outer trapped surfaces
• The Positive Mass Theorem with Angular Momentum and Charge for Manifolds with Boundary
• Rigidity of area-minimizing hyperbolic surfaces in three-manifolds