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Variance of the distance to the boundary of convex domains in $\mathbb{R}^{2}$ and $\mathbb{R}^{3}$

Authors :
Fletcher, Alastair N.
Fletcher, Alexander G.
Publication Year :
2024

Abstract

In this paper, we give for the first time a systematic study of the variance of the distance to the boundary for arbitrary bounded convex domains in $\mathbb{R}^2$ and $\mathbb{R}^3$. In dimension two, we show that this function is strictly convex, which leads to a new notion of the centre of such a domain, called the variocentre. In dimension three, we investigate the relationship between the variance and the distance to the boundary, which mathematically justifies claims made for a recently developed algorithm for classifying interior and exterior points with applications in biology.<br />Comment: 26 pages, 6 figures

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2407.12041
Document Type :
Working Paper