Fat equator effect and Minimality in immersions and submersions of the Sphere

2024/04/30 by Vicente Palmer, Garcia, Vicent Gimeno i, Palmer, Vicente
Engineering · Materials Science · Physics and Astronomy · #49Q15 #53A10 #58C35 #Differential Geometry (math.DG) #Experimental and Theoretical Physics Studies #FOS: Mathematics #Structural Analysis and Optimization #Textile materials and evaluations

paper · pdf · doi:10.48550/arxiv.2404.19416

openalex publication_date 2024/04/30 · openalex created_date 2024/05/03 · openalex updated_date 2026/07/28

Abstract

Inspired by the equatorial concentration of measure phenomenon in the sphere, a result which is deduced from the general, (and intrinsic), concentration of measure in \mathbbSⁿ(1), we describe in this paper an equatorial concentration of measure satisfied by the closed, (compact without boundary), isometric and minimal immersions x:Σ^m → \mathbbSⁿ(1), (m ≤ n), and by the minimal Riemannian submersions π: Σ^m → \mathbbSⁿ(1), (m ≥ n).

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