65 citations · 360 across the 54 of their papers we have counts for
47 papers · 1 filter
Isotropic submanifolds of and their focal sets
Nikos Georgiou, Brendan Guilfoyle, Morgan Robson
Families of oriented lines in are studied via their identification with submanifolds of . In particular, families of oriented lines which are orth…
The three obdurate conjectures of differential geometry
Brendan Guilfoyle, Wilhelm Klingenberg
We explore the role of symmetry in three obdurate conjectures of differential geometry: the Carathéodory, the Willmore and the Lawson Conjectures. All three Conjectures concern sur…
Minimal surfaces in the Riemannian product of surfaces
Nikos Georgiou, Brendan Guilfoyle
Minimal surfaces in the Riemannian product of surfaces of constant curvature have been considered recently, particularly as these products arise as spaces of oriented geodesics of…
From CT scans to 4-manifold topology
Brendan Guilfoyle
In this survey paper the ultrahyperbolic equation in dimension four is discussed from a geometric, analytic and topological point of view. The geometry centres on the canonical neu…
Parabolic evolution with boundary to the Bishop family of holomorphic discs
Brendan Guilfoyle, Wilhelm Klingenberg
It is proven that a definite graphical rotationally symmetric line congruence evolving under mean curvature flow with respect to the neutral Kaehler metric in the space of oriented…
A Conformal Mean Value Theorem for Solutions of the Ultrahyperbolic Equation
Guillem Cobos, Brendan Guilfoyle
Asgeirsson's theorem establishes a mean value property for solutions of the ultrahyperbolic equation. In the case of four variables, it states that the integrals of a solution over…