Sharp exponential asymptotic estimates for Jang’s equation

Schoen–Yau [Comm. Math. Phys. 79 (1981), no. 2, 231–260] showed that the graph of a blowup solution to Jang’s equation is asymptotic to cylinders over apparent horizons. In this paper, we will give a simple proof of the sharp upper and lower estimates for asymptotic rate. Furthermore, this proof can be applied to general blowup solutions to Jang’s equation that do not necessarily come from the Schoen–Yau regularization procedure.