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.
- The future is not always open, with Michael Kunzinger, Clemens Sämann and Roland Steinbauer. Preprint 2019. Submitted for publication. Available at arXiv:1901.07996.
- Inextendibility of spacetimes and Lorentzian length spaces, with Michael Kunzinger and Clemens Sämann, Annals of Global Analysis and Geometry 55 (2019), 133-147.
- The Hawking-Penrose singularity theorem for C^{1,1}-Lorentzian metrics, with Melanie Graf, Michael Kunzinger and Roland Steinbauer, Communications in Mathematical Physics 360 (2018), 1009-1042. [ pdf ]
- Valiente Kroon’s obstructions to smoothness at infinity, with K.P. Tod, General Relativity and Gravitation 47 (2015). [ pdf ]
- On differentiability of volume time functions, with P.T. Chruściel and E. Minguzzi, Annales Henri Poincaré 17 (2016), 2801-2824. [ pdf ]
- 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 ]
- On Lorentzian causality with continuous metrics, with P.T. Chruściel, Classical and Quantum Gravity 29 (2012), 145001. [ pdf ]
- 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 ]
- On Galilean connections and the first jet bundle, with B.C. Lackey, Central European Journal of Mathematics 10 (2012), 1889-1895. [ pdf ]
- Null injectivity estimate under an upper bound on the curvature, with P.G. LeFloch, Communications in Analysis and Geometry 22 (2014), 965-996. [ pdf ]
- Areas and volumes for null cones, Annales Henri Poincaré 12 (2011), 965-985. [ pdf ]
- Synthetic geometry and generalised functions, proceedings of the International Conference on Generalized Functions, Novi Sad Journal of Mathematics 41 (2011), 75-84. [ pdf ]
- Reducible connections and non-local symmetries of the self-dual Yang-Mills equations, Communications in Mathematical Physics 296 (2010), 429-446.[ pdf ]
- The ADHM construction and non-local symmetries of the self-dual Yang-Mills equations, Communications in Mathematical Physics 296 (2010), 405-428.[ pdf ]
- Block diagonalisation of four-dimensional metrics, with J.A. Vickers, Classical and Quantum Gravity 26 (2009), 235014. [ pdf ]
- The wave equation on singular space-times, with E. Mayerhofer and R. Steinbauer, Communications in Mathematical Physics 285 (2009), 399-420. [ pdf ]
- 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 ]
- 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 ]
- Coisotropic variational problems, with E. Musso, Journal of Geometry and Physics 50 (2004), 303-338. [ pdf ]
- Value distribution and spectral theory of Schrödinger operators with L^{2}-sparse potentials, with S.V. Breimesser and D.B. Pearson, Journal of Computational and Applied Mathematics 148 (2002), 307-322. [ pdf ]
- Grassmann structures and integrable systems, Journal of Geometry and Physics 40 (2001), 161-175. [ pdf ]
- A spinorial approach to Ricci-flat geometry, Classical and Quantum Gravity 16 (1999), 3419-3437. [ pdf ]
- Hypercomplex integrable systems, with I.A.B. Strachan, Nonlinearity 12 (1999), 1247-1261. [ pdf ]
- New Hamiltonians for gravity, with Ian. G. Moss, Physical Review D56 (1997), 6284-6292. [ pdf ]
- Lsdiff M and the Einstein equations, Classical and Quantum Gravity 13 (1996), L1-L5. [ pdf ]
- On self-dual gravity, Physical Review D48 (1993), 2606-2612. [ pdf ]
- Cosmic strings and chronology protection, Physical Review D47 (1993), 2388-2394. [ pdf ]
Additional material (lecture notes, seminar notes, unpublished papers, etc)
- A positive mass theorem for low-regularity Riemannian metrics, with N. Tassotti. Preprint arxiv:1408.6425. This paper will never appear, but I am leaving it here as it has been cited.
- A positive mass theorem for low-regularity metrics, with N. Tassotti. Announcement available at arxiv:1205.1302. This paper will not be published, but I am leaving it here as it has been cited.
- Notes on the initial value problem for the vacuum Einstein equations. Introductory lecture notes, Universität Wien, 2012.
- Notes on the conformal method. Introductory lecture notes, Universität Wien, 2012.
- Basic notes on wave equations. Introductory lecture notes, Universität Wien, 2012.
- Integrable systems and differential geometry. Habilitation thesis, Universität Wien, 2009.
- Injectivity radius estimates 1. Seminar notes (largely educational) Universität Wien, 2009.
- Global Lorentzian Geometry 2. Lecture notes, Universität Wien (2008).
- Global Lorentzian Geometry 1. Lecture notes, Universität Wien (2007/8).
- Fractals and Chaos. Lecture notes, University of Hull (1997-2002).
- Symplectic and Hyper-Kahler Quotient Constructions. Lecture notes, University of Hull (1997).
- Positive mass theorems in General Relativity. Lecture notes, University of Newcastle (1995).