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.
|Journal||Calculus of Variations and Partial Differential Equations|
|State||Published - Dec 2021|