Existence and Blow-Up Behavior for Solutions of the Generalized Jang Equation
Differential Geometry
2014-01-17 v2 General Relativity and Quantum Cosmology
Analysis of PDEs
Abstract
The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study of this equation, proving existence, regularity, and blow-up results. In particular, precise asymptotics for the blow-up behavior are given, and it is shown that blow-up solutions are not unique.
Cite
@article{arxiv.1206.0079,
title = {Existence and Blow-Up Behavior for Solutions of the Generalized Jang Equation},
author = {Qing Han and Marcus Khuri},
journal= {arXiv preprint arXiv:1206.0079},
year = {2014}
}
Comments
33 pages; final version