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math.DG2026
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…
physics.class-ph2026
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…
math.DG2026
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…