Equivariant index bound for min-max free boundary minimal surfaces

TL;DR

This paper establishes an upper bound on the equivariant index of free boundary minimal surfaces obtained through an equivariant min-max method, linking geometric symmetry with stability properties.

Contribution

It introduces a bound on the equivariant index for free boundary minimal surfaces constructed via an equivariant min-max approach, connecting symmetry groups with stability indices.

Findings

Equivariant index is bounded above by the number of parameters n.

Provides a link between symmetry group actions and stability of minimal surfaces.

Extends min-max theory to equivariant settings with boundary conditions.

Abstract

Given a three-dimensional Riemannian manifold with boundary and a finite group of orientation-preserving isometries of this manifold, we prove that the equivariant index of a free boundary minimal surface obtained via an equivariant min-max procedure \`a la Simon--Smith with $n$-parameters is bounded above by $n$.