On blowup of regularized solutions to Jang equation and constant expansion surfaces

Abstract

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.