Index and nullity of minimal surface doublings, I

2025/12/08 by Kapouleas, Nikolaos, Zou, Jiahua
Mathematics · #53A05 #53C21 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · doi:10.48550/arxiv.2512.07734

openalex publication_date 2025/12/08 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28

Abstract

We prove that for any large enough m ∈ℕ, the genus γ=m+1 equator-poles minimal surface doubling of the equatorial two-sphere Σ⁰ = \mathbbS²_eq in the round three-sphere \mathbbS³, which has two catenoidal bridges at the poles and m bridges equidistributed along the equatorial circle \mathscrC of Σ⁰ and was discovered in earlier work of Kapouleas, has index 2γ+5=2m+7 and nullity 6, and so it has no exceptional Jacobi fields and is C¹-isolated.

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