Year: 2026
Type: preprint
Abstract: 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 index of a linearly full minimal 2-sphere in the round 2n-sphere is at least n(n-1)(2n+1), with equality if and only if the 2-sphere is twistor-equivalent to the Boruvka sphere. Our techniques also apply more generally to give bounds for the Morse index and nullity for totally isotropic surfaces in the 2n-sphere.
Source: arXiv (Cornell University)
Authors: Ball, Gavin, Madnick, Jesse
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213524060