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. A positive mass theorem for low-regularity metrics, with N. Tassotti. Preprint arxiv:1205.1302. Submitted for publication. [ pdf ]
  2. Volume comparison for submanifolds in Lorentzian manifolds and singularity theorems, with Jan-Hendrik Treude. Preprint arxiv:1201.4249. ESI preprint 2351. Submitted for publication. [ pdf ]
  3. On Lorentzian causality with continuous metrics, with P.T. Chruściel. Preprint arxiv:1111.0400. To appear in Classical and Quantum Gravity. [ pdf ]
  4. New energy inequalities for tensorial wave equations on spacetimes that satisfy a one-sided bound, with A. Burtscher and P.G. LeFloch. Preprint arxiv:1105.0168. To appear in Communications in Partial Differential equations. [ pdf ]
  5. On Galilean connections and the first jet bundle, with B.C. Lackey. Preprint arxiv:math/9909148v1 (Revised 2011). Submitted for publication. [ pdf ]
  6. Null injectivity estimate under an upper curvature bound, with P.G. LeFloch. Preprint arxiv:1008.5167. Submitted for publication. [ pdf ]
  7. Areas and volumes for null cones, Annales Henri Poincaré 12, 965-985 (2011). [ pdf ]
  8. Synthetic geometry and generalised functions, proceedings of the International Conference on Generalized Functions, Novi Sad Journal of Mathematics 41, 75-84 (2011). [ pdf ]
  9. Reducible connections and non-local symmetries of the self-dual Yang-Mills equations, Communications in Mathematical Physics 296, 429-446 (2010).[ pdf ]
  10. The ADHM construction and non-local symmetries of the self-dual Yang-Mills equations, Communications in Mathematical Physics 296, 405-428 (2010).[ pdf ]
  11. Block diagonalisation of four-dimensional metrics, with J.A. Vickers, Classical and Quantum Gravity 26 (2009) 235014. [ pdf ]
  12. The wave equation on singular space-times, with E. Mayerhofer and R. Steinbauer, Communications in Mathematical Physics 285, 399-420 (2009). [ pdf ]
  13. Multidimensional integrable systems and deformations of Lie algebra homomorphisms, with M. Dunajski and I.A.B. Strachan, Journal of Mathematical Physics 48, 093502 (2007). [ pdf ]
  14. 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 ]
  15. Coisotropic variational problems, with E. Musso, Journal of Geometry and Physics 50, 303-338 (2004). [ pdf ]
  16. 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, 307-322 (2002). [ pdf ]
  17. Grassmann structures and integrable systems, Journal of Geometry and Physics 40, 161-75 (2001). [ pdf ]
  18. A spinorial approach to Ricci-flat geometry, Classical and Quantum Gravity 16, 3419-37 (1999). [ pdf ]
  19. Hypercomplex integrable systems, with I.A.B. Strachan, Nonlinearity 12, 1247-61 (1999). [ pdf ]
  20. New Hamiltonians for gravity, with Ian. G. Moss, Physical Review D56, 6284-92 (1997). [ pdf ]
  21. Lsdiff M and the Einstein equations, Classical and Quantum Gravity 13, L1-L5 (1996). [ pdf ]
  22. On self-dual gravity, Physical Review D48, 2606-12 (1993). [ pdf ]
  23. Cosmic strings and chronology protection, Physical Review D47, 2388-94 (1993). [ pdf ]

In Preparation

  1. A positive mass theorem for low-regularity Riemannian metrics, with N. Tassotti. [Expected completion: May/June 2012.]
  2. A global estimate of the Willmore energy of surfaces in Riemannian three-manifolds, with P.G. LeFloch. [Expected completion: May 2012.]

Work in progress

  1. Metrics with distributional curvature and Alexandrov spaces, with N. Tassotti.
  2. Dilated convergence of operators with applications to generalised point interactions, with C.J. Fewster.
  3. Isoperimetric quantities for null cones.

Additional material

  1. Positive mass theorems in General Relativity. Lecture notes, University of Newcastle.
  2. Symplectic and Hyper-Kahler Quotient Constructions. Lecture notes, University of Hull.
  3. Fractals and Chaos. Lecture notes, University of Hull.
  4. Global Lorentzian Geometry. Lecture notes, Universität Wien.
  5. Integrable systems and differential geometry. Habilitation thesis, Universität Wien, 2009.
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