Asian Journal of Mathematics

Volume 22 (2018)

Number 6

Curvature estimates for weakly stable surfaces of constant null expansions

Pages: 1089 – 1116

DOI: https://dx.doi.org/10.4310/AJM.2018.v22.n6.a6

Author

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

Abstract

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.

Keywords

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

2010 Mathematics Subject Classification

Primary 53C42. Secondary 53C80.

Full Text (PDF format)

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