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
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Knots, minimal surfaces and J-holomorphic curves.
Joel Fine.
arxiv:2112.07713 -
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 -
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 -
An ambient approach to conformal geodesics.
Joel Fine, Yannick Herfray.
Commun. Contemp. Math. 2021.
arxiv:1907.02701 -
Symplectic domination.
Joel Fine, Dmitri Panov.
Bull. London. Math. Soc. doi:10.1112/blms.12402, 2020.
arxiv:1905.05671 -
Examples of compact Einstein four-manifolds with negative curvature.
Joel Fine, Bruno Premoselli.
J. Amer. Math. Soc 33, 991-1038, 2020
arxiv:1802.00608 -
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 -
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 -
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 -
Asymptotically hyperbolic connections.
Joel Fine, Yannick Herfray, Kirill Krasnov, Carlos Scarinci.
Class. Quantum Grav. 33 (2016), no 18, 25pp.
arxiv:1512.07109 -
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 -
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 -
A gauge theoretic approach to the anti-self-dual Einstein equations.
Joel Fine.
arxiv:1111.5005 -
The diversity of symplectic Calabi-Yau six-manifolds.
Joel Fine, Dmitri Panov.
J. Toplogy, 6(1), 2013.
arxiv:1108.5994 -
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 -
Quantisation and the Hessian of Mabuchi energy.
Joel Fine.
Duke Math. J. 161(14), 2753-2798, 2012.
arxiv:1009.4543 -
Hyperbolic geometry and non-Kähler manifolds with trivial canonical bundle.
Joel Fine, Dmitri Panov.
Geometry and Topology, 14, 1723-1763, 2010.
arxiv:0905.3237 -
Calabi flow and projective embeddings.
Joel Fine.
J. Differential Geom. 84(3), 489-523, 2010.
arxiv:0811.0155 -
Building symplectic manifolds using hyperbolic geometry.
Joel Fine, Dmitri Panov.
J. Gökova Geom. Top., 124-136, 2009.
Preprint -
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 -
Toric anti-self-dual Einstein metrics via complex geometry.
Joel Fine.
Math. Ann. 340(1), 143-157, 2008.
arxiv:math/0609487 -
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 -
Toric anti-self-dual 4-manifolds via complex geometry.
Simon Donaldson, Joel Fine.
Math. Ann., 336(2), 281-309, 2006.
arxiv:math/0602423 -
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 -
Constant scalar curvature Kähler metrics on fibred complex surfaces.
Joel Fine.
J. Differential Geom., 68(3), 397-432, 2004.
arxiv:math/0401275 -
Constant scalar curvature metrics on fibred complex surfaces.
Joel Fine.
PhD thesis, University of London, 2004.
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