On uniqueness of free boundary minimal annuli in geodesic balls of \mathbbS³₊ and ℍ³

2025/03/21 by Lima, César
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2503.16763

openalex publication_date 2025/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider Σ an embedded free boundary minimal annulus in a geodesic ball in the round hemisphere \mathbbS³₊ or in the hyperbolic space ℍ³. Under the hypothesis of invariance due to an antipodal map on the geodesic ball and using the fact that this surface satisfies the Steklov problem with frequency, we prove that Σ is congruent to a critical rotational annulus.

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