A note on the index of closed minimal hypersurfaces of flat tori

TL;DR

This paper extends previous results to higher dimensions, establishing a lower bound on the Morse index of closed minimal hypersurfaces in flat tori based on their first Betti number.

Contribution

It generalizes earlier three-dimensional results to higher dimensions, providing an affine lower bound for the Morse index in terms of topological invariants.

Findings

Morse index is bounded below by a linear function of the first Betti number.

The result applies to closed minimal hypersurfaces in flat tori across various dimensions.

Provides a new link between topology and stability of minimal hypersurfaces.

Abstract

Generalizing earlier work by Ros in ambient dimension three, we prove an affine lower bound for the Morse index of closed minimal hypersurfaces inside a flat torus in terms of their first Betti number (with purely dimensional coefficients).