Year: 2026
Type: preprint
Abstract: In this short note we prove a rigidity result for orientable minimal submanifolds in the round sphere of the lowest non-trivial Morse index. In particular, we show that the only closed and connected $(2m-2)$-dimensional orientable minimal submanifolds in $\mathbb{S}^{2m}$ of index less than or equal to $2m+1$ are the totally geodesic spheres.
Source: arXiv (Cornell University)
Authors: Bernstein, Jacob, Ketover, Daniel
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214040471