On the Morse index of higher-dimensional free boundary minimal catenoids

2017/09/04 by Graham Smith, Ari Stern, Smith, Graham +5 · 1 citation
Computer Science · Mathematics · #53A10 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1709.00977

openalex publication_date 2017/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For all n, we define the n-dimensional critical catenoid M_n to be the unique rotationally symmetric, free boundary minimal hypersurface of non-trivial topology embedded in the closed unit ball in ℝⁿ⁺¹. We show that the Morse index MI(n) of M_n satisfies the following asymptotic estimate as n tends to infinity. lim_n→+∞(Log(MI(n)))/(√(n)Log(√(n))) = 1. We also study the numerical problem, providing exact values for the Morse index for n=2,⋯,100, together with qualitative studies of MI(n) and related geometric quantities for large values of n.

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Related

• The Morse index of the critical catenoid
• Minimal hypersurfaces of Morse index one
• Index estimates for free boundary minimal hypersurfaces
• Index of the critical catenoid
• Index growth not imputable to topology