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

Recent progress and problems on the Bartnik quasi-local mass

Pages: 851 – 873

DOI: https://dx.doi.org/10.4310/PAMQ.2019.v15.n3.a4


Michael T. Anderson (Department of Mathematics, Stony Brook University, Stony Brook, New York, U.S.A.)


This paper surveys recent progress on issues related to the Bartnik quasi-local mass $m_B$. In addition we formulate a number of new problems and conjectures regarding foundational properties of the mass $m_B$.

This work is dedicated with pleasure to Robert Bartnik in honor of his 60th birthday.

The author is partially supported by NSF Grant DMS 1607479.

Received 10 March 2019

Received revised 14 June 2019

Accepted 29 June 2019

Published 2 January 2020