Asian Journal of Mathematics

Volume 22 (2018)

Number 6

Curvature estimates for weakly stable surfaces of constant null expansions

Pages: 1089 – 1116



Zhuobin Liang (Department of Mathematics, Jinan University, Guangzhou, China)


In this paper, we prove by blow-up arguments the curvature estimates for weakly stable constant null expansion surfaces in Cauchy data set for the Einstein equation. This improves the sup-estimate by Andersson–Metzger [AM10] for the curvature of stable marginally outer trapped surfaces.


curvature estimates, null expansion, stability, convergence, blow-up

2010 Mathematics Subject Classification

Primary 53C42. Secondary 53C80.

The author is partially supported by National Science Foundation of China (grant 11171328, 11571345).

Received 15 February 2015

Accepted 9 March 2017

Published 6 February 2019