Mathematics > Differential Geometry
[Submitted on 30 Apr 2024]
Title:Fat equator effect and Minimality in immersions and submersions of the Sphere
View PDFAbstract: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 $\mathbb{S}^n(1)$, we describe in this paper an equatorial concentration of measure satisfied by the closed, (compact without boundary), isometric and minimal immersions $x:\Sigma^m \rightarrow \mathbb{S}^n(1)$, ($m \leq n$), and by the minimal Riemannian submersions $\pi: \Sigma^m \rightarrow \mathbb{S}^n(1)$, ($m \geq n$).
Submission history
From: Vicent Gimeno i Garcia [view email][v1] Tue, 30 Apr 2024 10:02:58 UTC (1,095 KB)
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