Jang's equation and its applications to marginally trapped surfaces

2010/06/23 by Lars Andersson, Andersson, Lars, Michael Eichmair +3 · 2 citations
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #gr-qc #math.AP

paper · pdf · doi:10.48550/arxiv.1006.4601

30 pages. To appear in the Proceedings of the Complex Analysis & Dynamical Systems IV Conference (Nahariya, Israel, May 2009)

openalex publication_date 2010/06/23 · arxiv created 2010/11/19 · arxiv updated 2010/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we survey some recent advances in the analysis of marginally outer trapped surfaces (MOTS). We begin with a systematic review of results by Schoen and Yau on Jang's equation and its relationship with MOTS. We then explain recent work on the existence, regularity, and properties of MOTS and discuss the consequences for the trapped region. We include an outlook with some directions for future research.

Cited by

• Area-charge inequality and local rigidity in charged initial data sets
• Penrose inequality for integral energy conditions

Related

• The Plateau problem for marginally outer trapped surfaces
• Jenkins-Serrin type results for the Jang equation
• Compactness Theorems and Degree Theory for MOTS
• Remarks on the stability operator for MOTS
• Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes