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.

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

References in corpus (2)

• Rigidity and Positivity of Mass for Asymptotically Hyperbolic Manifolds
• Rigidity of area-minimizing two-spheres in three-manifolds

Cited by in corpus (2)

• On the Positive Mass, Penrose, an ZAS Inequalities in General Dimension
• Rigidity of area-minimizing hyperbolic surfaces in three-manifolds