Papers

Published and Submitted Papers

Below are links to papers that I have published (or am about to publish). The preprint versions, to which there are also links, are generally identical to the published versions, sometimes with minor corrections.

  1. The Hawking-Penrose singularity theorem for C1,1-Lorentzian metrics, with Melanie Graf, Michael Kunzinger and Roland Steinbauer. Preprint arxiv:1706.08426. To appear in Communications in Mathematical Physics.
  2. Valiente Kroon’s obstructions to smoothness at infinity, with K.P. Tod, General Relativity and Gravitation 47 (2015). [ pdf ]
  3. A positive mass theorem for low-regularity Riemannian metrics, with N. Tassotti. Preprint arxiv: 1408.6425. Submitted for publication.
  4. On differentiability of volume time functions, with P.T. Chruściel and E. Minguzzi, Annales Henri Poincaré 17 (2016), 2801-2824. [ pdf ]
  5. Volume comparison for submanifolds in Lorentzian manifolds and singularity theorems, with Jan-Hendrik Treude, Annals of Global Analysis and Geometry 43 (2013), 233-251. [ pdf ]
  6. On Lorentzian causality with continuous metrics, with P.T. Chruściel, Classical and Quantum Gravity 29 (2012), 145001. [ pdf ]
  7. New energy inequalities for tensorial wave equations on spacetimes that satisfy a one-sided bound, with A. Burtscher and P.G. LeFloch, Communications in Partial Differential Equations 37 (2012), 1596-1619. [ pdf ]
  8. On Galilean connections and the first jet bundle, with B.C. Lackey, Central European Journal of Mathematics 10 (2012), 1889-1895. [ pdf ]
  9. Null injectivity estimate under an upper bound on the curvature, with P.G. LeFloch, Communications in Analysis and Geometry 22 (2014), 965-996. [ pdf ]
  10. Areas and volumes for null cones, Annales Henri Poincaré 12 (2011), 965-985. [ pdf ]
  11. Synthetic geometry and generalised functions, proceedings of the International Conference on Generalized Functions, Novi Sad Journal of Mathematics 41 (2011), 75-84. [ pdf ]
  12. Reducible connections and non-local symmetries of the self-dual Yang-Mills equations, Communications in Mathematical Physics 296 (2010), 429-446.[ pdf ]
  13. The ADHM construction and non-local symmetries of the self-dual Yang-Mills equations, Communications in Mathematical Physics 296 (2010), 405-428.[ pdf ]
  14. Block diagonalisation of four-dimensional metrics, with J.A. Vickers, Classical and Quantum Gravity 26 (2009), 235014. [ pdf ]
  15. The wave equation on singular space-times, with E. Mayerhofer and R. Steinbauer, Communications in Mathematical Physics 285 (2009), 399-420. [ pdf ]
  16. Multidimensional integrable systems and deformations of Lie algebra homomorphisms, with M. Dunajski and I.A.B. Strachan, Journal of Mathematical Physics 48 (2007), 093502. [ pdf ]
  17. Symmetries and moduli spaces of the self-dual Yang-Mills equations,in “Noncommutative Geometry and Physics”, Proceedings of the COE International Workshop, edited by Y. Maeda, N. Tose, N. Miyazaki, S. Watamura and D. Sternheimer (World Scientific, 2005) pp. 159-173. [ pdf ]
  18. Coisotropic variational problems, with E. Musso, Journal of Geometry and Physics 50 (2004), 303-338. [ pdf ]
  19. Value distribution and spectral theory of Schrödinger operators with L2-sparse potentials, with S.V. Breimesser and D.B. Pearson, Journal of Computational and Applied Mathematics 148 (2002), 307-322. [ pdf ]
  20. Grassmann structures and integrable systems, Journal of Geometry and Physics 40 (2001), 161-175. [ pdf ]
  21. A spinorial approach to Ricci-flat geometry, Classical and Quantum Gravity 16 (1999), 3419-3437. [ pdf ]
  22. Hypercomplex integrable systems, with I.A.B. Strachan, Nonlinearity 12 (1999), 1247-1261. [ pdf ]
  23. New Hamiltonians for gravity, with Ian. G. Moss, Physical Review D56 (1997), 6284-6292. [ pdf ]
  24. Lsdiff M and the Einstein equations, Classical and Quantum Gravity 13 (1996), L1-L5. [ pdf ]
  25. On self-dual gravity, Physical Review D48 (1993), 2606-2612. [ pdf ]
  26. Cosmic strings and chronology protection, Physical Review D47 (1993), 2388-2394. [ pdf ]

Additional material (lecture notes, seminar notes, etc)

  1. A positive mass theorem for low-regularity metrics, with N. Tassotti. Announcement available at arxiv:1205.1302.
  2. Notes on the initial value problem for the vacuum Einstein equations. Introductory lecture notes, Universität Wien, 2012.
  3. Notes on the conformal method. Introductory lecture notes, Universität Wien, 2012.
  4. Basic notes on wave equations. Introductory lecture notes, Universität Wien, 2012.
  5. Integrable systems and differential geometry. Habilitation thesis, Universität Wien, 2009.
  6. Injectivity radius estimates 1. Seminar notes (largely educational) Universität Wien, 2009.
  7. Global Lorentzian Geometry 2. Lecture notes, Universität Wien (2008).
  8. Global Lorentzian Geometry 1. Lecture notes, Universität Wien (2007/8).
  9. Fractals and Chaos. Lecture notes, University of Hull (1997-2002).
  10. Symplectic and Hyper-Kahler Quotient Constructions. Lecture notes, University of Hull (1997).
  11. Positive mass theorems in General Relativity. Lecture notes, University of Newcastle (1995).
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