Jang方程正则解的爆破与常数展开曲面
On blowup of regularized solutions to Jang equation and constant expansion surfaces
摘要：
本文分析了Jang方程正则解在视视界内的爆破行为。这扩展了Schoen-Yau在表观视野之外所做的分析。我们将采用两种自然的几何处理来爆破序列：膨胀和平移。首先，我们证明了适当平移的解决方案的限制是常数扩展面。其次，我们刻画了适当重标度解的极限。第三，我们讨论了由视界面包围的爆破区域的结构。最后，我们详细介绍了低速爆破的特殊情况。
英文摘要：
In this paper, we analyze the blowup behavior of regularized solutions to Jang equation inside apparent horizons. This extends the analyses outside apparent horizons done by Schoen-Yau. We will take two natural geometric treatments to blowup sequences: dilation and translation. First, we show that the limits of properly translated solutions are constant expansion surfaces. Second, we characterize the limits of properly rescaled solutions. Third, we discuss the structure of blowup regions enclosed by apparent horizons. Lastly, we elaborate on a special case of low-speed blowup.
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