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

Graham Smith, Ari Stern, Hung Tran, Detang Zhou

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


For all n, we define the n-dimensional critical catenoid Mn 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 Mn satisfies the following asymptotic estimate as n tends to infinity. Limn→+∞Log(MI(n))nLog(n)=1.We illustrate our results with an in-depth study of 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.

Original languageEnglish
Article number208
JournalCalculus of Variations and Partial Differential Equations
Issue number6
StatePublished - Dec 2021


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