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

Yu, Wenhua

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.

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More About This Work

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