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March 26, 20260 citationsOpen Access

Fat equator effect and minimality in immersions and submersions of the sphere

VGVicent Gimeno i GarciaVPVicente Palmer

Key Points

  • The aim is to explore the equatorial concentration of measure in minimal immersions and submersions of spheres, extending known results in differential geometry.
  • Analyzed closed isometric and minimal immersions of the sphere
  • Investigated minimal Riemannian submersions related to the sphere
  • Deduced results from intrinsic concentration of measure in spheres
  • Presented an equatorial concentration of measure applicable to minimal immersions
  • Outlined characteristics of minimal Riemannian submersions in the context of concentration phenomena
  • Established connections between immersion types and geometric properties of spheres

Abstract

Inspired by the equatorial concentration of measurephenomenon in the sphere, a result which is deducedfrom the general (and intrinsic), concentration of mea-sure in 𝕊𝑛 (1), we describe in this paper an equatorialconcentration of measure satisfied by the closed (com-pact without boundary), isometric and minimal immer-sions 𝑥 ∶ Σ 𝑚 → 𝕊 𝑛 (1), (𝑚 ⩽ 𝑛), and by the minimalRiemannian submersions 𝜋 ∶ Σ 𝑚 → 𝕊 𝑛 (1), (𝑚 ⩾ 𝑛).

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Cite This Study

Garcia et al. (2025) studied this question.

synapsesocial.com/papers/69c4cda5fdc3bde44891a564https://doi.org/10.1112/tlm3.70008digital
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Fat equator effect and minimality in immersions and submersions of the sphere2025
  2. 2Fat equator effect and Minimality in immersions and submersions of the Sphere2024
  3. 3Spheres with minimal equators2026
  4. 4Riemannian metrics on the sphere with Zoll families of minimal hypersurfaces2025 · 5 citations
  5. 5Minimal surfaces in H 3 (−1) via Willmore geometry, Gauss maps, meromorphic potentials, and algorithmic constructions2026