Stephen McCormick main menu

Home Research Teaching Prospective Students Assorted Documents Contact Me


I'm a Researcher in the Department of Mathematics at Uppsala University, specialising in geometric analysis, particularly when applied to problems coming from general relativity. I am particularly interested geometric inequalities and the problem of quasi-local mass.

Anyone interested in learning more about the geometric analytic aspects of general relativity, feel free to drop me an email. I'm always happy to chat!

You can find my articles via Google Scholar or arXiv. You can also follow me on Twitter (@Quasilocal).


6th Sept. - Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space (With A. Alaee and A. J. Cabrera Pacheco) accepted to appear in Transactions of the American Mathematical Society.


My specialisation is geometric analysis, however most of my research is focused on problems coming from general relativity. I am particularly interested in the problem of quasi-local mass (hence the registration of the domain, which amounts to determining a measure of the total mass or energy containing in a region of finite extend in some spacetime. Tangentially related to this, I am also interested in geometric inequalities analgous to isoperimetric-type inequalities, motivated by physical considerations via general relativity.

Publications and Preprints

  1. 20xx -- Quasi-local Penrose inequalities with electric charge, preprint. (With P.-N. Chen)
    arXiv preprint:2002.04557
  2. 20xx -- Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space, Trans. Amer. Math. Soc. (to appear). (With A. Alaee and A. J. Cabrera Pacheco)
    arXiv preprint:1911.12343
  3. 2020 -- Gluing Bartnik extensions, continuity of the Bartnik mass, and the equivalence of definitions, Pacific J. Math. 304(2). (arXiv link: 1805.09792)
  4. 2019 -- On the charged Riemannian Penrose inequality with charged matter, Class. Quantum Gravity, 37(1). (arXiv link:1907.07967)
  5. 2019 -- On the evolution of the spacetime Bartnik mass, Pure Appl. Math. Q. 15(3). (With P. Miao. Special issue in honour of Robert Bartnik.)
    ( arXiv link: 1902.02284)
  6. 2019 -- On a Penrose-like inequality in dimensions less than eight, Int. Math. Res. Not. 2019(7). (With P. Miao) (arXiv link:1701.04805)
  7. 2018 -- Asymptotically hyperbolic extensions and an analogue of the Bartnik mass, J. Geom. Phys. 132. (With A. J. Cabrera Pacheco, and C. Cederbaum) (arXiv link:1802.03331)
  8. 2018 -- On a Minkowski-like inequality for asymptotically flat static manifolds, Proc. Am. Math. Soc. 146 (arXiv link:1709.06550)
  9. 2017 -- Asymptotically flat extensions of CMC Bartnik data, Class. Quantum grav. 34(10) (With A. J. Cabrera Pacheco, C. Cederbaum, and P. Miao) (arXiv link:1612.05241)
  10. 2017 -- The asymptotically flat scalar-flat Yamabe problem with boundary, J. Geom. Anal. 27(3) (arXiv link:1603.05318)
  11. 2015 -- A note on mass-minimising extensions, Gen. Rel. Grav. 47(12).
    DOI: 10.1007/s10714-015-1993-2 (arXiv link:1501.05045)
  12. 2014 -- First law of black hole mechanics as a condition for stationarity, Phys. Rev. D 90.
    DOI: 10.1103/PhysRevD.90.104034 (arXiv link:1406.7480)
  13. 2014 -- The phase space for the Einstein-Yang-Mills equations and the first law of black hole thermodynamics, Adv. Theor. Math. Phys. 18.
    DOI: 10.4310/ATMP.2014.v18.n4.a2 (arXiv link:1302.1237)


Autumn 2020, I am teaching 1MA212 - Geometri och analys III. Current students should refer to Studium for all course materials.

Prospective Students

I am more than happy to discuss project possibilities with current and prospective students, both in relation to studying at Uppsala or abroad. You can write me an email with any questions. Here is some information for prospective students at each level, who wish to study in Uppsala:


At Uppsala University PhD candidates are considered employees, as is the norm in Sweden. This means that the recruitment process is similar to recruitment of other research staff, making the positions as competetive as they are attractive. When positions are available, they are advertised here.


Information regarding the Master's Programme in Mathematics at Uppsala University can be found here.
There are also several scholarships available for international students, which can be found here.
I am available for supervision of Master's projects. Contact me if you are interested and I can provide some suggestions for project topics.


For current Bachelor's students in mathematics or physics at Uppsala, I am available to supervise Bachelor's theses. Contact me to discuss potential projects.

Assorted Documents