Index Estimates for Free Boundary Constant Mean Curvature Surfaces

TL;DR

This paper establishes a lower bound on the Morse index of free boundary constant mean curvature surfaces based on their topological features, providing new insights into their stability properties.

Contribution

It introduces a linear lower bound on the Morse index in terms of genus and boundary components for these surfaces, advancing understanding of their stability.

Findings

Morse index is bounded below by a linear function of genus.

The bound applies to surfaces in Euclidean space and the unit sphere.

Provides new tools for analyzing stability of free boundary CMC surfaces.

Abstract

In this paper, we consider compact free boundary constant mean curvature surfaces immersed in a mean convex body of the Euclidean space or in the unit sphere. We prove that the Morse index is bounded from below by a linear function of the genus and number of boundary components.