TY - JOUR
T1 - On the Morse index of higher-dimensional free boundary minimal catenoids
AU - Smith, Graham
AU - Stern, Ari
AU - Tran, Hung
AU - Zhou, Detang
N1 - Funding Information:
The second author was in part supported by the Simons Foundation (award #279968). The third author would like to thank Prof. Richard Schoen for helpful discussions. The fourth author was partially supported by CNPq and FAPERJ of Brazil. Finally, we would like to thank the anonymous referee for many helpful comments.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2021/12
Y1 - 2021/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85113633580&partnerID=8YFLogxK
U2 - 10.1007/s00526-021-02049-8
DO - 10.1007/s00526-021-02049-8
M3 - Article
AN - SCOPUS:85113633580
SN - 0944-2669
VL - 60
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 6
M1 - 208
ER -