标题： 广义Jang方程解的存在性与爆破行为 显示英文标题

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

摘要： 广义Jang方程是在试图证明爱因斯坦方程一般初始数据背景下彭罗斯不等式的尝试中引入的。本文对该方程进行了广泛的研究，证明了存在性、正则性和爆破结果。特别是，给出了爆破行为的精确渐近性，并且表明爆破解不是唯一的。 显示英文摘要

摘要： 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.