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

2024/11/05 by Seemungal, Luca, Sharp, Ben
#49Q05 #53A10 #53C42 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.02932

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.

Related

• Index Estimates for Surfaces with Constant Mean Curvature in 3-dimensional Manifolds
• Lower bounds for Morse index of constant mean curvature tori
• Lower bounds for the index of compact constant mean curvature surfaces in \mathbb R³ and \mathbb S³
• Bounds for the Morse index of free boundary minimal surfaces
• On the Index of Constant Mean Curvature Hypersurfaces