Morse Index Bound for Minimal Torus

TL;DR

This paper proves that the Morse index of a min-max conformal harmonic torus, constructed via harmonic replacement methods, is bounded by one, providing a key stability estimate for such minimal surfaces.

Contribution

It establishes a Morse index bound of one for min-max conformal harmonic tori, extending previous min-max constructions to a new stability result.

Findings

Morse index of the min-max conformal harmonic torus is at most one

Extension of min-max construction methods to conformal harmonic tori

Provides stability insights for minimal tori in geometric analysis

Abstract

The min-max construction of minimal spheres using harmonic replacement is introduced by Colding and Minicozzi and generalized by Zhou to conformal harmonic torus. We prove that the Morse index of the min-max conformal harmonic torus is bounded by one.