Index growth not imputable to topology

2024/07/15 by Alessandro Carlotto, Carlotto, Alessandro, Mario B. Schulz +3 · 2 citations
Mathematics · Medicine · #Adrenal and Paraganglionic Tumors #Advanced Topology and Set Theory #Differential Geometry (math.DG) #FOS: Mathematics #Hormonal Regulation and Hypertension

paper · pdf · doi:10.48550/arxiv.2407.11147

openalex publication_date 2024/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

We employ partitioning methods, in the spirit of Montiel--Ros but here recast for general actions of compact Lie groups, to prove effective lower bounds on the Morse index of certain families of closed minimal hypersurfaces in the round four-dimensional sphere, and of free boundary minimal hypersurfaces in the Euclidean four-dimensional ball. Our analysis reveals, in particular, phenomena of linear index growth for sequences of minimal hypersurfaces of fixed topological type, in strong contrast to the three-dimensional scenario.

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