10 citations · 15 across the 11 of their papers we have counts for
14 papers
The second variation of 2-spheres in the 2n-sphere
Gavin Ball, Jesse Madnick
We prove sharp upper and lower bounds for the Morse index and nullity of linearly full branched minimal 2-spheres in the round 2n-sphere. In particular, we show that the Morse inde…
The Maxwell Conjecture is False
Philip Arathoon, Gavin Ball, Matthew D. Kvalheim
We exhibit a configuration of five point charges in Euclidean space whose electrostatic potential admits at least 24 critical points all of which are non-degenerate. Maxwell's conj…
The Morse index of constant curvature 2-spheres
Gavin Ball, Jesse Madnick
In the round -sphere, we calculate the Morse index and nullity of all immersed minimal 2-spheres having constant Gauss curvature. We also obtain bounds on the stability index of…
Static solutions to symplectic curvature flow in dimension four
Gavin Ball
This article studies special solutions to symplectic curvature flow in dimension four. Firstly, we derive a local normal form for static solutions in terms of holomorphic data and…
The Morse index of quartic minimal hypersurfaces
Gavin Ball, Jesse Madnick, Uwe Semmelmann
The homogeneous minimal hypersurfaces in have , or distinct (constant) principal curvatures. While the Morse index and nullity have been calculated for all s…
A Spinorial Hopf Differential for Associative Submanifolds
Gavin Ball, Jesse Madnick
Given a CMC surface in , its traceless second fundamental form can be viewed as a holomorphic section called the Hopf differential. By analogy, we show that for an associative…