2019 Theses Doctoral

# Blowup rate control for solution of Jang's equation and its application on Penrose inequality

We prove that the blowup term of a blowup solution of Jang's equation on an initial data set (M,g,k) near an arbitrary strictly stable MOTS Σ is exactly −1/√λlog τ, where τ is the distance from Σ and λ is the principal eigenvalue of the MOTS stability operator of Σ. We also prove that the gradient of the solution is of order τ^(-1). Moreover, we apply these results to get a Penrose-like inequality under additional assumptions.

## Files

- Yu_columbia_0054D_15162.pdf application/pdf 355 KB Download File

## More About This Work

- Academic Units
- Mathematics
- Thesis Advisors
- Wang, Mu-Tao
- Degree
- Ph.D., Columbia University
- Published Here
- April 12, 2019