Existence and Blow-Up Behavior for Solutions of the Generalized Jang Equation

DOI10.1080/03605302.2013.837919zbMath1319.35261arXiv1206.0079OpenAlexW2963020346MaRDI QIDQ5746985

Qing Han, Marcus A. Khuri

Publication date: 11 February 2014

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.0079

zbMATH Keywords

blow-up solutionsPenrose inequalitygeneralized Jang equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) Degenerate elliptic equations (35J70) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) PDEs in connection with relativity and gravitational theory (35Q75) Boundary value problems on manifolds (58J32) Blow-up in context of PDEs (35B44)

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Cites Work

• Jenkins-Serrin-type results for the Jang equation
• P.D.E.'s which imply the Penrose conjecture
• Blowup of Jang's equation at outermost marginally trapped surfaces
• A generalization of Hawking's black hole topology theorem to higher dimensions
• Rigidity of marginally trapped surfaces and the topology of black holes
• A Jang equation approach to the Penrose inequality
• The area of horizons and the trapped region
• Proof of the positive mass theorem. II
• On the proof of the positive mass conjecture in general relativity
• A new proof of the positive energy theorem.
• Jang's equation and its applications to marginally trapped surfaces
• Sobolev and isoperimetric inequalities for riemannian submanifolds
• The Jang equation, apparent horizons and the Penrose inequality
• On the Penrose inequality for charged black holes
• Rigidity in the positive mass theorem with charge

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