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

Abstract

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
Volume60
Issue number6
DOIs
StatePublished - Dec 2021

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