Index estimates for constant mean curvature surfaces in three-manifolds by energy comparison

TL;DR

This paper establishes a linear upper bound on the Morse index of closed constant mean curvature surfaces in three-manifolds, relating it to topological and energetic properties.

Contribution

It introduces a new energy comparison method to bound the Morse index of CMC surfaces in three-manifolds.

Findings

Morse index is linearly bounded by genus and branch points.

The bound depends on a Willmore-type energy.

Provides a new approach to stability analysis of CMC surfaces.

Abstract

We prove a linear upper bound on the Morse index of closed constant mean curvature (CMC) surfaces in orientable three-manifolds in terms of genus, number of branch points and a Willmore-type energy.