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Welcome

I'm a mathematician 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. I am employed as a researcher at the University of Regensburg however I am more regularly found as a guest at KTH Royal Institute of Technology in Stockholm.

Anyone interested in learning more about the geometric or 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) where I try to post light-hearted mathematics and physis but inevitably get sucked into discussions on current issues.

Research

My specialisation is geometric analysis, however most of my research is inspired and guided by general relativity. One topic I am particular interested in is the problem of quasi-local mass, which amounts to determining a measure of the total mass or energy contained in a region of finite extent in some spacetime. I am also interested in geometric inequalities -- in the spirit of isoperimetric-type inequalities -- motivated by physical considerations via general relativity.

Publications

  1. 2021 -- Quasi-local Penrose inequalities with electric charge, Int. Math. Res. Not. rnab215. (With P.-N. Chen)
    https://doi.org/10.1093/imrn/rnab215 (arXiv link:2002.04557)
  2. 2021 -- Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space, Trans. Amer. Math. Soc. 374. (With A. Alaee and A. J. Cabrera Pacheco)
    https://doi.org/10.1090/tran/8297 (arXiv link:1911.12343)
  3. 2021 -- The Hilbert manifold of asymptotically flat metric extensions, Gen. Relativ. Gravit. 53(14).
    https://doi.org/10.1007/s10714-021-02785-4 (Open Access)
  4. 2020 -- Gluing Bartnik extensions, continuity of the Bartnik mass, and the equivalence of definitions, Pacific J. Math. 304(2).
    doi.org/10.2140/pjm.2020.304.629 (arXiv link: 1805.09792)
  5. 2019 -- On the charged Riemannian Penrose inequality with charged matter, Class. Quantum Gravity, 37(1).
    doi.org/10.1088/1361-6382/ab50a8 (arXiv link:1907.07967)
  6. 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.)
    (doi.org/10.4310/PAMQ.2019.v15.n3.a6 arXiv link: 1902.02284)
  7. 2019 -- On a Penrose-like inequality in dimensions less than eight, Int. Math. Res. Not. 2019(7). (With P. Miao)
    doi.org/10.1093/imrn/rnx181 (arXiv link:1701.04805)
  8. 2018 -- Asymptotically hyperbolic extensions and an analogue of the Bartnik mass, J. Geom. Phys. 132. (With A. J. Cabrera Pacheco, and C. Cederbaum)
    doi.org/10.1016/j.geomphys.2018.06.010 (arXiv link:1802.03331)
  9. 2018 -- On a Minkowski-like inequality for asymptotically flat static manifolds, Proc. Am. Math. Soc. 146
    doi.org/10.1090/proc/14047 (arXiv link:1709.06550)
  10. 2017 -- Asymptotically flat extensions of CMC Bartnik data, Class. Quantum grav. 34(10) (With A. J. Cabrera Pacheco, C. Cederbaum, and P. Miao)
    doi.org/10.1088/1361-6382/aa6921 (arXiv link:1612.05241)
  11. 2017 -- The asymptotically flat scalar-flat Yamabe problem with boundary, J. Geom. Anal. 27(3)
    doi.org/10.1007/s12220-017-9760-0 (Open Access)
  12. 2015 -- A note on mass-minimising extensions, Gen. Rel. Grav. 47(12).
    DOI: 10.1007/s10714-015-1993-2 (Open Access)
  13. 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)
  14. 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 (Open Access)

Teaching

I am not currently teaching any courses.

Assorted Documents