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An Isoperimetric Result on High-Dimensional Spheres
- Publication Year :
- 2018
-
Abstract
- We consider an extremal problem for subsets of high-dimensional spheres that can be thought of as an extension of the classical isoperimetric problem on the sphere. Let $A$ be a subset of the $(m-1)$-dimensional sphere $\mathbb{S}^{m-1}$, and let $\mathbf{y}\in \mathbb{S}^{m-1}$ be a randomly chosen point on the sphere. What is the measure of the intersection of the $t$-neighborhood of the point $\mathbf{y}$ with the subset $A$? We show that with high probability this intersection is approximately as large as the intersection that would occur with high probability if $A$ were a spherical cap of the same measure.<br />Comment: arXiv admin note: text overlap with arXiv:1701.02043
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1811.10533
- Document Type :
- Working Paper