58 citations · 178 across the 23 of their papers we have counts for
18 papers · 1 filter
Non-degeneracy of Poincaré-Einstein four-manifolds satisfying a chiral curvature inequality
Joel Fine
A Poincaré-Einstein metric is called non-degenerate if there are no non-zero infinitesimal Einstein deformations of , in Bianchi gauge, that lie in . We prove that a 4-…
Knots, minimal surfaces and J-holomorphic curves
Joel Fine
Let be a knot in the 3-sphere, viewed as the ideal boundary of hyperbolic 4-space . We prove that the number of minimal discs in with ideal boundar…
A report on the hypersymplectic flow
Joel Fine, Chengjian Yao
This article discusses a relatively new geometric flow, called the hypersymplectic flow. In the first half of the article we explain the original motivating ideas for the flow, com…
Local rigidity of Einstein 4-manifolds satisfying a chiral curvature condition
Joel Fine, Kirill Krasnov, Michael Singer
Let (M,g) be a compact oriented Einstein 4-manifold. Write R-plus for the part of the curvature operator of g which acts on self-dual 2-forms. We prove that if R-plus is negative d…
An ambient approach to conformal geodesics
Joel Fine, Yannick Herfray
Conformal geodesics are distinguished curves on a conformal manifold, loosely analogous to geodesics of Riemannian geometry. One definition of them is as solutions to a third order…
Examples of compact Einstein four-manifolds with negative curvature
Joel Fine, Bruno Premoselli
We give new examples of compact, negatively curved Einstein manifolds of dimension . These are seemingly the first such examples which are not locally homogeneous. Our metrics a…