Pure and Applied Mathematics Quarterly

Volume 15 (2019)

Number 3

Special Issue: In Honor of Robert Bartnik (Part 2 of 2)

Guest Editors: Piotr T. Chruściel, Greg Galloway, Jim Isenberg, Pengzi Miao, Mu-Tao Wang, and Shing-Tung Yau

Positivity of Brown–York mass with quasi-positive boundary data

Pages: 967 – 982

DOI: https://dx.doi.org/10.4310/PAMQ.2019.v15.n3.a8


Yuguang Shi (Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing, China)

Luen-Fai Tam (Institute of Mathematical Sciences and Department of Mathematics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong)


In this short note, we prove positivity of Brown–York mass under quasi-positive boundary data which generalizes some previous results by the authors. The corresponding rigidity result is obtained.


Brown–York mass, quasi-positive, nonnegative scalar metrics

2010 Mathematics Subject Classification

Primary 53C20. Secondary 83C99.

The authors would like to dedicate this paper to Robert Bartnik on the occasion of his sixtieth birthday.

The research of Y. Shi was partially supported by NSFC 11671015 and 11731001. The research of L.-F. Tam was partially supported by Hong Kong RGC General Research Fund #CUHK 14301517.

Received 1 February 2019

Received revised 18 April 2019

Accepted 2 May 2019

Published 2 January 2020