7 citations
4 papers
Fredholm-Regularity of Holomorphic Discs in Plane Bundles over Compact Surfaces
Brendan Guilfoyle, Wilhelm Klingenberg
We study the space of holomorphic discs with boundary on a surface in a real 2-dimensional vector bundle over a compact 2-manifold. We prove that, if the ambient 4-manifold admits…
On Isolated Umbilic Points
Brendan Guilfoyle
Counter-examples to the famous conjecture of Caratheodory, as well as the bound on umbilic index proposed by Hamburger, are constructed with respect to Riemannian metrics that are…
Mean Curvature Flow of Compact Spacelike Submanifolds in Higher Codimension
Brendan Guilfoyle, Wilhelm Klingenberg
We prove long-time existence for mean curvature flow of a smooth -dimensional spacelike submanifold of an dimensional manifold whose metric satisfies the timelike curvatur…
Hopf hypersurfaces in spaces of oriented geodesics
Nikos Georgiou, Brendan Guilfoyle
A Hopf hypersurface in a (para-)Kaehler manifold is a real hypersurface for which one of the principal directions of the second fundamental form is the (para-)complex dual of the n…