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

2011/01/28 by Gregory J. Galloway, Galloway, Gregory J. · 4 citations
Mathematics · Physics and Astronomy · #53C20 #83C57 #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1101.5549

openalex publication_date 2011/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the proof of the positive mass conjecture in general relativity
• Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature
• Area-minimizing projective planes in three-manifolds

Cited by

• Stability of weighted minimal hypersurfaces under a lower 1-weighted Ricci curvature bound
• The index of the cosmological horizon and the area-charge-inequality
• On the Positive Mass, Penrose, an ZAS Inequalities in General Dimension
• Rigidity of area-minimizing hyperbolic surfaces in three-manifolds
• Area-charge inequality and local rigidity in charged initial data sets

Related

• Geometry of non-compact minimal and marginally outer-trapped surfaces in asymptotically flat manifolds
• Minimal Surfaces from Rigid Motions
• Stable free boundary surfaces with constant extrinsic curvature in 3-dimensional space forms
• Rigidity of stable marginally outer trapped surfaces in initial data\n sets
• Geometric relations of stable minimal surfaces and applications