Papers

Below is a list of the research, survey articles and lecture notes I have written. You can also find all of my research articles on the ArXiv.

Research articles

  1. Convergence of the hypersymplectic flow on T4 with T3-symmetry.
    Joel Fine, Weiyong He and Chengjian Yao
    arxiv:2404/15016
  2. Non-degeneracy of Poincaré-Einstein four-manifolds satisfying a chiral curvature inequality.
    Joel Fine.
    J. Geom. Anal. 33, article 249, 2023
    arxiv:2212.00526
  3. Knots, minimal surfaces and J-holomorphic curves.
    Joel Fine.
    arxiv:2112.07713
  4. A report on the hypersymplectic flow.
    Joel Fine, Chengjian Yao
    Pure Appl. Math. Q., Issue in honour of Simon Donaldson, 15:4, 1219-1260, 2019.
    arxiv:2001.11755
  5. Local rigidity of Einstein 4-manifolds satisfying a chiral curvature condition.
    Joel Fine, Kirill Krasnov, Michael Singer.
    Math. Ann. 379, pages 569-588, 2021.
    arxiv:1910.09790
  6. An ambient approach to conformal geodesics.
    Joel Fine, Yannick Herfray.
    Commun. Contemp. Math. 24:03 article number 2150009, 2022.
    arxiv:1907.02701
  7. Symplectic domination.
    Joel Fine, Dmitri Panov.
    Bull. London. Math. Soc. doi:10.1112/blms.12402, 2020.
    arxiv:1905.05671
  8. Examples of compact Einstein four-manifolds with negative curvature.
    Joel Fine, Bruno Premoselli.
    J. Amer. Math. Soc 33, 991-1038, 2020
    arxiv:1802.00608
  9. Hypersymplectic 4-manifolds, the G2-Laplacian flow and extension assuming bounded scalar curvature.
    Joel Fine, Chengjian Yao.
    Duke Math. J. 167(18), 3533-3589, 2018
    arxiv:1704.07620
  10. The space of hyperkähler metrics on a 4-manifold with boundary.
    Joel Fine, Jason D. Lotay, Michael Singer.
    Forum of Mathematics, Sigma vol 5, 2017 50pp.
    arxiv:1603.08170
  11. Limits of Riemannian 4-manifolds and the symplectic geometry of their twistor spaces.
    Joel Fine.
    Transactions of the LMS 4(1), 100-109, 2017.
    arxiv:1602.03829
  12. Asymptotically hyperbolic connections.
    Joel Fine, Yannick Herfray, Kirill Krasnov, Carlos Scarinci.
    Class. Quantum Grav. 33 (2016), no 18, 25pp.
    arxiv:1512.07109
  13. Circle invariant fat bundles and symplectic Fano 6-manifolds.
    Joel Fine, Dmitri Panov.
    J. London Math. Soc. 91(3) 709-730, 2015.
    arxiv:1407.0840
  14. A gauge theoretic approach to Einstein 4-manifolds.
    Joel Fine, Kirill Krasnov, Dmitri Panov.
    New York J. Math. 20 293-323, 2014.
    arxiv:1312.2831
  15. A gauge theoretic approach to the anti-self-dual Einstein equations.
    Joel Fine.
    arxiv:1111.5005
  16. The diversity of symplectic Calabi-Yau six-manifolds.
    Joel Fine, Dmitri Panov.
    J. Toplogy, 6(1), 2013.
    arxiv:1108.5994
  17. The Hamiltonian geometry of the space of unitary connections with symplectic curvature.
    Joel Fine.
    J. Symplectic Geom. 12(1) 105-123, 2014.
    arxiv:1101.2420
  18. Quantisation and the Hessian of Mabuchi energy.
    Joel Fine.
    Duke Math. J. 161(14), 2753-2798, 2012.
    arxiv:1009.4543
  19. Hyperbolic geometry and non-Kähler manifolds with trivial canonical bundle.
    Joel Fine, Dmitri Panov.
    Geometry and Topology, 14, 1723-1763, 2010.
    arxiv:0905.3237
  20. Calabi flow and projective embeddings.
    Joel Fine.
    J. Differential Geom. 84(3), 489-523, 2010.
    arxiv:0811.0155
  21. Building symplectic manifolds using hyperbolic geometry.
    Joel Fine, Dmitri Panov.
    J. Gökova Geom. Top., 124-136, 2009.
    Preprint
  22. Symplectic Calabi-Yau manifolds, minimal surfaces and the hyperbolic geometry of the conifold.
    Joel Fine, Dmitri Panov.
    J. Differential Geom., 82(1), 155-205, 2009.
    arxiv:0802.3648
  23. Toric anti-self-dual Einstein metrics via complex geometry.
    Joel Fine.
    Math. Ann. 340(1), 143-157, 2008.
    arxiv:math/0609487
  24. A note on positivity of the CM line bundle.
    Joel Fine, Julius Ross.
    Int. Math. Res. Not., Article ID 95875, 14pp, 2006.
    arxiv:math/0605302
  25. Toric anti-self-dual 4-manifolds via complex geometry.
    Simon Donaldson, Joel Fine.
    Math. Ann., 336(2), 281-309, 2006.
    arxiv:math/0602423
  26. Fibrations with constant scalar curvature Kähler metrics and the CM-line bundle.
    Joel Fine.
    Math. Res. Lett., 14(2), 239-247, 2007.
    arxiv:math/0510075
  27. Constant scalar curvature Kähler metrics on fibred complex surfaces.
    Joel Fine.
    J. Differential Geom., 68(3), 397-432, 2004.
    arxiv:math/0401275
  28. Constant scalar curvature metrics on fibred complex surfaces.
    Joel Fine.
    PhD thesis, University of London, 2004.
    pdf ps

Survey articles and notes