On stable constant mean curvature surfaces in S2 X R and H2 X R

TL;DR

This paper investigates the properties and stability of compact constant mean curvature surfaces within the product spaces S2 X R and H2 X R, expanding understanding of their geometric behavior.

Contribution

It provides new insights into the stability conditions and classifications of constant mean curvature surfaces in these specific Riemannian product spaces.

Findings

Characterization of stable CMC surfaces in S2 X R and H2 X R

Identification of conditions for stability in these manifolds

Extension of known results to broader classes of Riemannian 3-manifolds

Abstract

We study stable compact constant mean curvature surfaces in the product spaces S2 X R and H2 X R and in some other Riemannian 3-manifolds.